[SOLVED] Congruent Modulo

rexsi · March 27th 2006, 03:57 PM

I have an assignment due tommorow and I am completely lost I was wondering if anyone could give me a hand hehe.

The two silly questions I am stuck on are:

Find all numbers between 10 and 20 which are congruent to 173 modulo 3

and.....

Find all numbers between 10 and 20 which are congruent to -173 modulo 4

**ThePerfectHacker** · March 27th 2006, 06:25 PM

Originally Posted by rexsi

I have an assignment due tommorow and I am completely lost I was wondering if anyone could give me a hand hehe.

The two silly questions I am stuck on are:

Find all numbers between 10 and 20 which are congruent to 173 modulo 3

and.....

Find all numbers between 10 and 20 which are congruent to -173 modulo 4

You need,
$x\equiv 173 \mod 3$
But,
$173\equiv 2\mod 3$
Thus, (transitive property of congruences)
$x\equiv 2\mod 3$
But, $10\leq x\leq 20$ .
Thus, $x=11,14,17,20$
-----------
You need,
$x\equiv -173 \mod 4$
But,
$-173\equiv 3\mod 4$
Thus, (transitive property of congruences)
$x\equiv 3\mod 4$
But, $10\leq x\leq 20$
Thus, $x=11,15,19$

$\mathbb{Q}.\mathbb{E}.\mathbb{D}$

Thread: [SOLVED] Congruent Modulo

LinkBack

Thread Tools

Display

[SOLVED] Congruent Modulo

Similar Math Help Forum Discussions

[SOLVED] congruent modulo n

congruent to modulo; the fundamentals

prove that the binomial (p-1) over k is congruent to -1^k modulo p

[SOLVED] Prove that a^p is congruent to b^p (mod p^2) if the same is true mod p

[SOLVED] [SOLVED] Prove side of regular inscribed hexagon congruent to radius

Search Tags