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Sum of its digits plus the square of its units digit

Source: South African MO 2010 Q1

May 26, 2012
number theory unsolvednumber theory

Problem Statement

For a positive integer nn, S(n)S(n) denotes the sum of its digits and U(n)U(n) its unit digit. Determine all positive integers nn with the property that n=S(n)+U(n)2.n = S(n) + U(n)^2.
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