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a^2_1+ a^2_2+ a^2_3+ a^2_4+ a^2_5= b^2, not all odd`

Source: Eotvos 1931 p2

September 10, 2024
number theoryoddPerfect Square

Problem Statement

Let a12+a22+a32+a42+a52=b2a^2_1+ a^2_2+ a^2_3+ a^2_4+ a^2_5= b^2, where a1a_1, a2a_2, a3a_3, a4a_4, a5a_5, and bb are integers. Prove that not all of these numbers can be odd.
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