Proof of x = 0 modulo 3 only if the sum of its digits 0 modulo 3
41563
Prove that if the sum of digits of a number is divisible by 3, so is the number itself.
89265
Proving that $x - \frac{x^3}{3!} 0$
63409
If $x^2+ax+b=0$ has a rational root, show that it is in fact an integer
28218
Elementary proof for $\sqrt[3]{xyz} \leq \dfrac{x+y+z}{3}$
68233
Fermat's little theorem's proof for a negative integer
122076
A one line proof that one is zero using Mathematica 10
46158
A positive integer is divisible by $3$ iff 3 divides the sum of its digits
57981
Alternative proof of $a\times0= 0$
76032
Prove that if m is a square integer then m is neither congruent to 2 modulo 5 nor congruent to 3 modulo 5
52454
If $x^3 =x$ then $6x=0$ in a ring
30261
How can I find all integers $x≠3$ such that $x−3|x^3−3$
66451
In a ring, how do we prove that a * 0 = 0?
56828
A combinatorial proof that the alternating sum of binomial coefficients is zero
50226
Prove the identity $\sum_{k=0}^{n}\sum_{r=0}^{k} \binom{k}{r} \binom{n}{k} = 3^n$
26301
Prove that $x^3 \equiv x \bmod 6$ for all integers $x$
33735
The square of an integer is congruent to 0 or 1 mod 4
127816
Number theory proof mod p