List questions from congruences

Published on 17 Mar 2014 - 19:16

72

Views

Do we not have to follow Euclidean division strictly when doing modulo operations?

Published on 17 Mar 2014 - 19:50

35

Views

Verifying that $11^{λ(m)+1} ≡ 11 \pmod m$ for $m = 41 \cdot 11$

Published on 17 Mar 2014 - 21:46

163

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Solving for $3^x - 1 = 2^y$

Published on 20 Mar 2014 - 8:09

1.3k

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Finding the remainder of $49!$ when divided by $53$

Published on 20 Mar 2014 - 16:48

180

Views

Fermat's Little Theorem not useful as $p\rightarrow\infty$

Published on 23 Mar 2014 - 14:23

61

Views

Doubt concerning Fermat's little theorem with a nonprime number

Published on 23 Mar 2014 - 19:54

47

Views

Solving for $5^a+1 = 2\cdot3^b$ beyond $5+1=6$

Published on 23 Mar 2014 - 21:53

439

Views

Solve $33x≡9$ (mod 29)

Published on 24 Mar 2014 - 1:36

494

Views

Is there an integer $y>0$ such that for all $x>y$, at least $4$ of $x+1, x+2, x+3, x+4, x+5$ are divisible by a prime greater than $5$?

Published on 24 Mar 2014 - 2:00

2.5k

Views

How can I solve $4x + 51y = 9$ using congruences?

Published on 25 Mar 2014 - 3:24

137

Views

How do you compute $1+x+\cdots+x^7=0 \mod 40$?

Published on 26 Mar 2014 - 0:21

965

Views

How to prove that the product of two congruence classes mod p are congruent to another product of congruence classes

Published on 26 Mar 2014 - 4:48

45

Views

Is it true that given a positive integer $c$, there is at most one solution for $p^a - q^b = c$ where $p, q$ are primes and $p > q$

Published on 26 Mar 2014 - 8:10

276

Views

Integer solutions of $800000007 = x^2+y^2+z^2$

Published on 27 Mar 2014 - 7:33

List Question

Even, Odd, Congruent

Do we not have to follow Euclidean division strictly when doing modulo operations?

Verifying that $11^{λ(m)+1} ≡ 11 \pmod m$ for $m = 41 \cdot 11$

Solving for $3^x - 1 = 2^y$

Finding the remainder of $49!$ when divided by $53$

Fermat's Little Theorem not useful as $p\rightarrow\infty$

Doubt concerning Fermat's little theorem with a nonprime number

Solving for $5^a+1 = 2\cdot3^b$ beyond $5+1=6$

Solve $33x≡9$ (mod 29)

Is there an integer $y>0$ such that for all $x>y$, at least $4$ of $x+1, x+2, x+3, x+4, x+5$ are divisible by a prime greater than $5$?

How can I solve $4x + 51y = 9$ using congruences?

How do you compute $1+x+\cdots+x^7=0 \mod 40$?

How to prove that the product of two congruence classes mod p are congruent to another product of congruence classes

Is it true that given a positive integer $c$, there is at most one solution for $p^a - q^b = c$ where $p, q$ are primes and $p > q$

Integer solutions of $800000007 = x^2+y^2+z^2$

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