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a^4 + 4a^3 + 11a^2 + 6a+ 2 a sum of 3 squares and divisible by 4 for odd a

Source: Spanish Mathematical Olympiad 1981 P8

December 23, 2022
number theorySum of Squaresdivisible

Problem Statement

If aa is an odd number, show that a4+4a3+11a2+6a+2a^4 + 4a^3 + 11a^2 + 6a+ 2 is a sum of three squares and is divisible by 44.