#1126 · Number Theory · Divisibility

Square of repeated digit in consecutive base

Let $r$ , $s = r + 1$ , $q = r + 2$ be three consecutive integers. Prove that in base $s$ the square of the number consisting of four repeated digits $r$ (i.e. $r r r r_{s}$ ) equals $r r r r q 000 1_{s}$ .

~8 minProof · checked by AIbase arithmeticdigit patterns

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. VII. Scales of Notation, Examples VII.b, No. 34

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