26 | Observations on a theory of Fermat and others on looking at prime numbers |
29 | On the solution of a problem of Diophantus |
36 | Solution of problems of arithmetic of finding numbers which, when divided by given numbers, leave given remainders |
54 | A proof of certain theorems regarding prime numbers |
98 | The proofs of some arithmetic theorems |
100 | On Amicable Numbers |
134 | Theorems on divisors of numbers |
152 | On amicable numbers |
158 | Various analytical observations about combinations |
164 | Theorems about the divisors of numbers contained in the form paa ± qbb |
167 | On the solution of a most difficult problem proposed by Fermat |
175 | Discovery of an extraordinary law of numbers in relation to the sum of their divisors |
191 | On the partitions of numbers |
228 | On numbers which are the sum of two squares |
241 | Proof of a theorem of Fermat that every prime number of the form 4n+1 is the sum of two squares |
242 | Proof of a theorem of Fermat that every number whether whole or fraction is the sum of four or fewer squares |
243 | Observations on the sums of divisors |
244 | A demonstration of a theorem on the order observed in the sums of divisors |
253 | On indeterminate problems which appear to be quite determinate |
255 | General solution of certain Diophantine problems, which are ordinarily thought to admit only special solutions |
256 | Example of the use of observation in pure mathematics |
262 | Theorems about the remainders left by division by powers |
270 | The solution of a problem about searching for three numbers, of which the sum and not only their product but the sum of their products two apiece, are square numbers |
271 | Demonstration of a new method in the Theory of Arithmetic |
272 | A reinforcement of some arithmetic theorems, supported by several demonstrations |
279 | On the resolution of formulas of squares of indeterminates by integral numbers |
283 | On very large prime numbers |
323 | Concerning the use of a new algorithm to solve the Pell problem |
369 | How very large numbers are to be tested for whether they are prime or not |
394 | On the partition of numbers into a number of parts of a given type |
405 | A solution of a problem about two numbers which are searched for, of which their product, increased or decreased by their sum or difference, will be a square |
427 | An investigation of a certain Diophantine problem |
428 | Observations about two biquadratics, of which the sum is able to be resolved into two other biquadratics |
445 | Proof that every integer is the sum of four squares |
449 | Demonstrations about the residues resulting from the division of powers by prime numbers |
451 | A solution of the problem of finding a triangle, in which the lines from each angle bisecting the opposite sides are rational |
452 | The resolution of the equation Ax^{2} + 2Bxy + Cy^{2} + 2Dx + 2Ey + F = 0 by rational and integral numbers |
454 | On the resolution of irrationals by continued fractions, where a certain minor new and singular type is set forth |
461 | Extract of a letter by Mr. Euler to Mr. Bernoulli father concerning the memoire published by them in 1771, p. 318 |
466 | A singular Diophantine problem |
467 | On the table of prime numbers continued up to one million and beyond, in which at once all the non-prime numbers are expressed by their smallest divisors |
474 | A solution of several Diophantine problems |
498 | Extract of a letter from Mr. Euler to Mr. Beguelin from May 1778 |
515 | De casibus quibusdam maxime memorabilibus in analysi indeterminata, ubi imprimis insignis usus calculi angulorum in analysi Diophantea ostenditur |
523 | On three square numbers, of which the sum and the sum of products two apiece will be a square |
541 | The expansion of the infinite product (1-x)(1-xx)(1-x^{3})(1-x^{4})(1-x^{5}) etc. into a single series |
542 | On the remarkable properties of the pentagonal numbers |
552 | Observations about the division of squares by prime numbers |
554 | A more exact disquisition about the residues remaining from the division of squares and of higher powers by prime numbers |
556 | On the criteria of whether equation fxx + gyy = hxx admits a resolution or not |
557 | De quibusdam eximiis proprietatibus circa divisores potestatum occurrentibus |
558 | Proposita quacunque protressione ab unitate incipiente, quaeritur quot eius terminos a dminimum addi oporteat, ut omnes numeri producantur |
559 | New assistance for solving the formula axx + 1 = yy |
560 | Miscellaneous analyses |
564 | Speculations about certain outstanding properties of numbers |
566 | De inductione ad plenam certitudinem evehenda |
586 | Considerations about a theorem of Fermat on the resolution of numbers into polygonal numbers |
591 | On the relation between three and more quantities which are to be instituted |
596 | On the sum of the series of numbers of the form 1/3 - 1/5 + 1/7 + 1/11 - 1/13 ... in which the prime numbers of the form 4n-1 have positive signs, and those of the form 4n+1 have negative signs |
598 | De insigni promotione scientiae numerorum |
610 | New demonstrations about the divisors of numbers of the form xx + nyy |
683 | On a singular type of Diophantine questions and a most recondite method by which they are to be resolved |
696 | On the cases in which the form x^{4} + kxxyy + y^{4} is permitted to be reduced to a square |
699 | Inquiring on whether or not the number 100009 is prime |
702 | De novo genere quaestionum arithmeticarum pro quibus solvendis certa methodus adhuc desideratur |
708 | On forms of the type mxx + nyy for exploring prime numbers by idoneals of them with remarkable properties |
713 | An investigation of a triangle in which the distances of the angles from the center of gravity of it may be expressed rationally |
715 | On various ways of examining very large numbers, for whether or not they are primes |
716 | The resolution of the Diophantine formula ab(maa+nbb) = cd(mcc+ndd) by rational numbers |
718 | An easy method of finding several rather large prime numbers |
719 | A more general method by which all adequately large numbers may be scrutinized for whether or not they are prime |
725 | An illustration of a paradox about the idoneal, or suitable, numbers |
732 | An easier solution of a Diophantine problem about triangles, in which those lines from the vertices which bisect the opposite sides may be expressed rationally |
739 | An easy rule for Diophantine problems which are to be resolved quickly by integral numbers |
744 | On divisors of numbers of the form mxx + nyy |
748 | Investigatio quadrilateri, in quo singularum angulorum sinus datam inter se teneant rationem, ubi artificia prorsus singularia in Analysi Diophantea occurrunt |
753 | Solution succincta et elegans problematis, quo quaeruntur tres numeri tales, ut tam summae quam differentiae binorum sint quadrata |
754 | On a problem of geometry resolved by Diophantine analysis |
755 | On cases for which the formula x^{4} + mxxyy + y^{4} can be reduced to a square |
758 | De binis formulis speciei xx + myy et xx + nyy inter se concordibus et discordibus |
763 | On finding three or more numbers, the sum of which is a square, while the sum of the squares is a fourth power |
764 | An easy resolution to a most difficult question, where this most general form vvzz(axx+byy)^{2} + Δxxyy(avv+bzz)^{2} is required to be reduced to a square |
769 | A solution to a problem of Fermat, on two numbers of which the sum is a square and the sum of their squares is a biquadrate, inspired by the Illustrious La Grange |
772 | On a notable advancement of Diophantine analysis |
773 | A solution of a most difficult problem, in which the two forms aaxx + bbyy et aayy + bbxx must be rendered into squares |
774 | An investigation of two numbers of the form xy(x^{4}-y^{4}), of which the product and the quotient will be a square |
775 | On two numbers, of which the sum when increased or decreased by the square of one of them produces a square |
776 | Elucidations about two sums of pairs of biquadratics, which are mutually equal |
777 | On the resolution of the equation 0 = a + bx + cy + dxx + exy + fyy + gxxy + hyy + ixxyy by rational numbers |
778 | A new and easy method for reducing cubic and biquadratic forms to squares |
792 | Tractatus de numerorum doctrina capita sedecim, quae supersunt |
793 | Thoughts concerning Diophantine analysis |
796 | Research into the problem of three square numbers such that the sum of any two less the third one provides a square number |
797 | Further and curious research into the problem of four positive numbers and an arithmetical proportion such that the sum of any two is always a square number |
798 | On amicable numbers |
799 | A fragment of a commentary, the most part on finding the relation between the sides of triangles of which the area is able to be expressed rationally, and of triangles in which the lines from each angle bisecting the opposite line are rationals |