MathsGee Answers - Recent questions tagged number-theory
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Powered by Question2AnswerProve Wilson's Theorem
https://mathsgee.com/29385/prove-wilsons-theorem
Prove Wilson's TheoremMathematicshttps://mathsgee.com/29385/prove-wilsons-theoremFri, 04 Jun 2021 08:35:37 +0000What is the remainder when 44! is divided by 47
https://mathsgee.com/29381/what-is-the-remainder-when-44-is-divided-by-47
What is the remainder when $44!$ is divided by $47$<br />
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$$\dfrac{44!}{47}$$Mathematicshttps://mathsgee.com/29381/what-is-the-remainder-when-44-is-divided-by-47Wed, 02 Jun 2021 14:18:30 +0000Use the converse of Wilson's Theorem to determine the primality of 13
https://mathsgee.com/29363/use-the-converse-of-wilsons-theorem-determine-the-primality
Use the converse of Wilson's Theorem to determine the primality of $13$Mathematicshttps://mathsgee.com/29363/use-the-converse-of-wilsons-theorem-determine-the-primalityTue, 01 Jun 2021 16:59:16 +0000Solve the following congruence
https://mathsgee.com/29362/solve-the-following-congruence
Use Euler's Theorem to solve the folllowing congruence<br />
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$ 7x \equiv 5 (mod \ 24)$Mathematicshttps://mathsgee.com/29362/solve-the-following-congruenceTue, 01 Jun 2021 15:50:56 +0000Use Euler's Theorem
https://mathsgee.com/29361/use-eulers-theorem
Use Euler's Theorem to find the least positive residue of $3^{100000} \ modulo \ 35 $Mathematicshttps://mathsgee.com/29361/use-eulers-theoremTue, 01 Jun 2021 15:35:27 +0000Prove the following
https://mathsgee.com/29360/prove-the-following
Let $n,k \in \mathbb{R}^+ $ such that $ k =(p-1)q +r, 0 \leq r \leq p$<br />
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Prove that $ n^k \equiv n^r \ (mod \ p)$Mathematicshttps://mathsgee.com/29360/prove-the-followingTue, 01 Jun 2021 14:36:14 +0000Prove that \(left \frac{5}{p} \right) = 1 if and only if p \eqiuv \pm 1 \pmod{4} for p prime
https://mathsgee.com/27189/prove-that-left-frac-right-if-and-only-if-eqiuv-pmod-for-prime
<p>Prove that <span class="math-tex">\(\left( \frac{5}{p} \right) = 1\)</span> if and only if <span class="math-tex">\(p \equiv \pm 1 \pmod{4}\)</span>, for <span class="math-tex">\(p\)</span> prime</p>Mathematicshttps://mathsgee.com/27189/prove-that-left-frac-right-if-and-only-if-eqiuv-pmod-for-primeFri, 30 Apr 2021 19:39:04 +0000Show that if p is an odd prime, then $2 \cdot (p-3)! \equiv -1 \pmod{p}$
https://mathsgee.com/27188/show-that-if-p-is-an-odd-prime-then-2-cdot-p-3-equiv-1-pmod-p
Show that if \(p\) is an odd prime, then \(2\cdot (p-3)! \equiv -1 \pmod{p}\)Mathematicshttps://mathsgee.com/27188/show-that-if-p-is-an-odd-prime-then-2-cdot-p-3-equiv-1-pmod-pFri, 30 Apr 2021 19:22:20 +0000Given that $p$ is a prime, and $p \mid a^n$, prove that $p^n \mid a^n$.
https://mathsgee.com/27176/given-that-p-is-a-prime-and-p-mid-a-n-prove-that-p-n-mid-a-n
Given that $p$ is a prime, and $p \mid a^n$, prove that $p^n \mid a^n$.Mathematicshttps://mathsgee.com/27176/given-that-p-is-a-prime-and-p-mid-a-n-prove-that-p-n-mid-a-nFri, 30 Apr 2021 10:54:32 +0000