#1130 · Number Theory · Divisibility

Triple‑repeat divisibility

Show that any decimal number formed by writing three digits $a, b, c$ and then repeating them in the same order, i.e. the number $ab c ab c$ , is divisible by $7$ , $11$ , and $13$ .

~6 minProof · checked by AIrepeating blocksprime factors

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. VII. Scales of Notation, Examples VII.b, No. 38

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