[Math] Perfect square with digit-sum 15

elementary-number-theorynatural numbers

Prove that there is not a single natural number $N$ with sum of digits equal to 15 that is the square of an integer.

Best Answer

Hint: If the sum of the digits is $15$, then $N$ is divisible by $3$, if $N$ is a square then it is also divisble by $9$, if $N$ is divisble by $9$, then the sum of digits...

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