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Prove that the numbers of the sequence $121,12321,1234321,\cdots$ are each a perfect square of an odd integer.

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Note by Sandeep Bhardwaj
2 years, 2 months ago

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we can prove it by induction (n=1,.......,9) for n=1, it is a perfect square of 1 let it be true for n, so 123.....n........321 = m^2 for some m an odd integer see that 100m^2 + 20m + 1 = 123......(n+1).......321 therefore (10m+1)^2=123........(n+1)...........321 ,proved see that 10m+1 is odd

- 2 years, 2 months ago