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The number n in n^2 (Posted on 2019-04-11) Difficulty: 3 of 5
5 is in 52=25, but 5 is at the end of 25. 10 is in 102=100, but 100 ends in 0. What is the smallest positive integer n such that n is in n2, and there is at least one nonzero digit after n in n2?

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Some Thoughts Puzzle Thoughts Comment 3 of 3 |
The smallest positive integer in full conformity with the provisions of the puzzle under reference is 3792 since:
3792^2 = 14379264, where:
(i) the number 3792 is contained within its square
(ii) the string '3792' appearing within the square is followed by '2', a nonzero number.

*** I will now essayer de trouver une solution analytique and will posit the same when my efforts in that direction reach fruition.

Edited on June 2, 2022, 11:58 pm
  Posted by K Sengupta on 2022-06-02 23:57:49

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