List questions from congruences

Published on 12 Feb 2014 - 16:31

119

Views

Find $r$ for $3^{574} + 26^{1347}\equiv r\mod 5$

Published on 12 Feb 2014 - 18:29

70

Views

Find $r\equiv 9^{137}*x^{51}+36^{1003}(\mod 7)$

Published on 13 Feb 2014 - 8:13

70

Views

Find all the $a$ such $539|a3^{253}+5^{44}$

Published on 13 Feb 2014 - 13:57

63

Views

Find m $\in \mathbb N$ that as condition is product of $3$ primes and the equation $x^2 +1 \equiv 0 \pmod{m}$ has $8$ solutions modulo $m$

Published on 17 Feb 2014 - 16:39

48

Views

Why do we need the extra assertion in this question?

Published on 17 Feb 2014 - 20:17

80

Views

Show that two (p-1) th roots of unity cannot be congruent modulo p.

Published on 18 Feb 2014 - 18:59

77

Views

Congruence of $n^n$ modulo 5

Published on 18 Feb 2014 - 19:50

69

Views

Theorem of Jacobi: $(2k+1)! + (-1)^{\eta} \equiv 0 \ (\operatorname{mod} p)$

Published on 29 Mar 2026 - 7:40

48

Views

A way of finding $x \in \mathbb{Z}$, congruency

Published on 20 Feb 2014 - 3:03

200

Views

Show $x^2+y^2 \equiv1\pmod p$ has $p-1$ solutions if $p \equiv1\pmod4$ and...

Published on 20 Feb 2014 - 12:32

62

Views

Composite Integers modulo zero

Published on 21 Feb 2014 - 15:32

552

Views

Finding the inverse of a congruence

Published on 31 Mar 2026 - 6:04

1.2k

Views

Is an equivalence class same as residue class?

Published on 22 Feb 2014 - 9:48

54

Views

Solution of a congruence equation in a PID

Published on 31 Mar 2026 - 17:48

List Question

Find $r\in\Bbb Z$ for $4^{451}\equiv r\mod 7$

Find $r$ for $3^{574} + 26^{1347}\equiv r\mod 5$

Find $r\equiv 9^{137}*x^{51}+36^{1003}(\mod 7)$

Find all the $a$ such $539|a3^{253}+5^{44}$

Find m $\in \mathbb N$ that as condition is product of $3$ primes and the equation $x^2 +1 \equiv 0 \pmod{m}$ has $8$ solutions modulo $m$

Why do we need the extra assertion in this question?

Show that two (p-1) th roots of unity cannot be congruent modulo p.

Congruence of $n^n$ modulo 5

Theorem of Jacobi: $(2k+1)! + (-1)^{\eta} \equiv 0 \ (\operatorname{mod} p)$

A way of finding $x \in \mathbb{Z}$, congruency

Show $x^2+y^2 \equiv1\pmod p$ has $p-1$ solutions if $p \equiv1\pmod4$ and...

Composite Integers modulo zero

Finding the inverse of a congruence

Is an equivalence class same as residue class?

Solution of a congruence equation in a PID

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