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a^4+b^3+c^2+d =\overline{cd} (2023 May Olympiad L1 p2)

Source:

March 24, 2024
number theory

Problem Statement

We say that a four-digit number abcd‾\overline{abcd} is slippery if the number a4+b3+c2+da^4+b^3+c^2+d is equal to the two-digit number cd‾\overline{cd}. For example, 20232023 slippery, since 24+03+22+3=232^4 + 0^3 + 2 ^2 + 3 = 23. How many slippery numbers are there?
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