the number of different least positive residues modu $p^2$ of $x^p-1$ is $= p+1$?How prove such that $2^n-8$ is divisible by $n$, and $n$ has least three distinct prime factors.Show the number of quadratic residues $a$ modulo $p$ with $1leq aleq p-1$ is $(p-1)/2$why this $ab+k,bc+k,ca+k$ always perfect squareNumber theory contradictionInfinitely many primes such that $a^(p-1)/d equiv 1 bmod p$Fermat's Little theorem and least value of powershow that there exist infinitely many positive integers $k$ such $p^n|k^k-a$if $nnmid 2^n+1, n|2^2^n+1+1$ show that the $3^kcdot p$ is good postive integers numbersthere are at least $fracp+12$ integers $d$, with $0 leq d < p$, so that the equation $x^3+x=d pmod p$ has a root$pmod p$is it true that there **exist at least** a prime $P$ of the form $p_0^alpha_0p_1^alpha_1p_2^alpha_2…p_k^alpha_k+1$ ?
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