How to prove that all integers with more than 1 digits, minus the sum of their digits result in $\mod 3=0$?
73020
Every integer is congruent to the sum of its digits mod 9
26301
Prove that $x^3 \equiv x \bmod 6$ for all integers $x$
105225
Number Theory: Complete set of residues modulo $n$
149481
Number theory counting sums of squares modulus
127183
Proof: For all integers $x$ and $y$, if $x^3+x = y^3+y$ then $x = y$
24301
Can a finite sum of square roots be an integer?
72437
Sum of the digits of a perfect square
139
Prove or disprove: For every integer a, if a is not congruent to 0 (mod 3), the a^2 is congruent to 1 (mod 3)
87626
Why are all $n$, s.t. the sum of digits of $n$ and $n^2$ coincide, $\equiv 0,1 \bmod 9$
853
Write down the sum of sum of  sum of digits of $4444^{4444}$
3632
Basic number theory proofs
30136
Proof that a Combination is an integer
119433
How to find modulo of large numbers like $9801\! \pmod {\!32}$
105719
Complex numbers modulo integers
158124
Sum of all the positive integers problem
44182
Proving that an integer is even if and only if it is not odd
131625
Expressing an integer as the sum of three squares