olymmath

BALTIC-WAY 2002 Problem 3

  • Answer

Find all sequences a0⩽a1⩽a2⩽…a_{0} \leqslant a_{1} \leqslant a_{2} \leqslant \ldots of real numbers such that

am2+n2=am2+an2a_{m^{2}+n^{2}}=a_{m}^{2}+a_{n}^{2}

for all integers m,n⩾0m, n \geqslant 0.

Dataset text NuminaMath olympiads. Quoted with source.

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a_{n} \equiv 0, a_{n} \equiv \frac{1}{2}, a_{n}=n

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