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1

Part of 1998 Mexico National Olympiad

Problems(1)

infinitely pairs of consecutive lucky numbers in number theory

Source: Mexican Mathematical Olympiad 1998 OMM P1

7/28/2018
A number is called lucky if computing the sum of the squares of its digits and repeating this operation sufficiently many times leads to number 11. For example, 19001900 is lucky, as 1900→82→68→100→11900 \to 82 \to 68 \to 100 \to 1. Find infinitely many pairs of consecutive numbers each of which is lucky.
number theoryDigitsconsecutive