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Questions tagged [infinite-descent]

Infinite descent, also named Fermat's descent, is a technique to prove that a diophantine equation has no solutions by construction a 'smaller' solution from a given one.

Infinite descent, also named Fermat's descent, is a technique to prove that a diophantine equation has no solutions by construction a 'smaller' solution from a given one.

51 questions
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Right angled triangles

Are right angled triangles the only triangles that can be divided into 2,4,8,16- - (2^n)smaller triangles, each being the same shape as the original? In other words is it the only one where infinite descent occurs?
Terence Coates
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Let there be $2n+1$ integers such that when one of them is removed, the sum can be divided into $2$ groups each with $n$ integers.

Let $a_1,a_2,\cdots,a_{2n+1}$ be integers such that, if any one of them is removed, the remaining ones can be divided into two sets of $n$ integers with equal sum. Prove $a_1 = a_2 = \cdots = a_{2n+1}$ $Note:-$ The solution is mentioned in this…
arnav_de
  • 699