Diophantine equations

three positive integers, the squares of two of which sum to the square of the third

polynomial equation with integer solutions

formula relating two numbers and their greatest common divisor

mathematical equation, specifically a kind of Diophantine equation

theorem about consecutive powers

non-negative integer, the representation of whose square in that base can be split into two parts that add up to the original number again

disproved mathematical conjecture

A proof by contradiction used to show that a statement cannot be true for all numbers. If a statement is true for one number, it will also be true for a smaller number, up to infinity, leading to a contradiction and disproving the original statement.

the Diophantine problem of finding an integer, whose factorial plus one is a perfect square

a problem in number theory with a very large solution, attributed to Archimedes

unproven statement in number theory

conjecture in number theory

an integer x, y, or z that can solve the Markov equation x^2 + y^2 + z^2 = 3xyz

conjecture

Mathematics problem

the Diophantine equation 2ⁿ−7=𝑥²

the mathematical problem of characterizing which integers are representable as sums of three cubes of integers

exponential function

cyclic algorithm to solve indeterminate quadratic equations

proof technique

problem in number theory

principle that an integer equation can be solved by piecing together modular solutions

non-existence proof in number theory, the only complete proof left by Pierre de Fermat

diophantine equation attributed to Jacobi and Madden

number-theoretic conjecture that states that 𝑘 people running around a circular track with distinct speeds will each be, at some point, separated by ¹⁄ₖ from every other runner

four integers where the sum of the squares of three equal the square of the fourth

theorem

conjecture

theorem giving conditions for existence of solutions to the Diophantine equation ax²+by²+cz²=0

set of integers, the lengths of the sides of a triangle with a 60° angle

statement about the representability of zero by odd degree forms

data tree in which each node branches to three subsequent nodes with the infinite set of all nodes giving all (and only) primitive Pythagorean triples without duplication

tuple of numbers (a₁, a₂, …) such that aᵢaⱼ+1 is a perfect square for every i<j

solution of some Diophantine equation

number theory problem

type of equation with integer coefficients

type of elliptic curve