Natural number is written with only 0, 3, 7. Prove that a perfect square does not exist. How do I prove this statement?

1 Answer
May 3, 2018

The answer:


All perfect squares end in 1, 4, 5, 6, 9, 00 (or 0000, 000000 and etc.)
A number which ends in 2, #color(red)3#, #color(red)7#, 8 and only #color(red)0# is not a perfect square.
If the natural number consists of these three digits (0, 3, 7), it is inevitable that the number has to end in one of them. It was like that this natural number cannot be a perfect square.