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q_1^4+q_2^4+q_3^4+q_4^4+q_5^ is product of 2 even consecutive

Source: 2011 Saudi Arabia Pre-TST February 1.2

January 1, 2022

number theory

Problem Statement

Find all primes

q_1, q_2, q_3, q_4, q_5

such that

q_1^4+q_2^4+q_3^4+q_4^4+q_5^4

is the product of two consecutive even integers.