Prove that 9 | $a_k +... +a_1+a_0$ implies that 9 | $a_k 10^k +... + a_1 10^1 + a_o 10^0$
117380
Divisibility Rule for 9
120309
Number Theory Inequality Proof
153763
Prove that $a_1!\cdots a_k! < n!$ whenever $a_1+\cdots+a_k < n$
111505
Proof $\binom{p-1}{k}\equiv (-1)^k \mod{p}$
83752
If $p + q = 1$ prove that for any natural $n, m$ following is true: $(1 - p^n)^m + (1 - q^m)^n \ge 1$
25981
Prove that $\sum_{k=0}^n a_k x^k = 0$ has at least $1$ real root if $\sum_{k=0}^n \frac{a_k}{k+1} = 0$
568
Consider a set $A$ of $10$ integers, $A = \{a_1,a_2, \ldots ,a_{10}\}$. Prove that there is at least one subset of $A$ whose sum is divisible by $10$.
33177
All numbers of form $10^{k} + 1$ are composite for $k{\gt}2$ proof
103545
Prove "casting out nines" of an integer is equivalent to that integer modulo 9
46831
Show that $ a，b, \sqrt{a}+ \sqrt{b} \in\mathbb Q \implies \sqrt{a},\sqrt{b} \in\mathbb Q $
7843
Show that order of $a^k$
6777
Showing $(a^{2}+2)(b^{2}+2)(c^{2}+2)\geq 9(ab+bc+ca)$
55266
Prove that $(n+1)^{n-1}<n^n$
5708
Prove that if $k\ge 1\,$ and $\,a^k\equiv 1\pmod{\! n}$ then $\gcd(a,n)=1$
76696
Using induction to prove $2^{n-1}(1 + a_1a_2\ldots a_n) \geq (1+a_1)(1+a_2)\ldots(1+a_n)$ for $a_i \geq 1$
101159
Prove If a ≡ b (mod n) and c ≡ d (mod n), then a + c ≡ b + d (mod n)
68971
Elementary approach to proving that a group of order 9 is Abelian