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n = a^2 + b^3 + c^3 + d^5

Source: 2020 Grand Duchy of Lithuania, Mathematical Contest p4 (Baltic Way TST)

October 3, 2020
number theory

Problem Statement

We shall call an integer n cute if it can be written in the form n=a2+b3+c3+d5n = a^2 + b^3 + c^3 + d^5, where a,b,ca, b, c and dd are integers. a) Determine if the number 20202020 is cute. b) Find all cute integers