Princeton Review Error : Congruences Page 225

Forum for the GRE subject test in mathematics.
Legendre
Posts: 217
Joined: Wed Jun 03, 2009 1:05 am

Princeton Review Error : Congruences Page 225

Postby Legendre » Mon Sep 21, 2009 3:05 am

Princeton Review, rule 3 :

For any positive integer c, the statement

'a is congruent to b (mod n)'
<=>
'a is congruent to b (mod cn)'


Counter-example :

5 congruent 2 (mod 3)

Let c = 2.

5 congruent 2 (mod 9) is FALSE. Since (5-2) = 3 is not divisible by 9.

hopeful_statguy
Posts: 7
Joined: Sun Sep 13, 2009 5:45 pm

Re: Princeton Review Error : Congruences Page 225

Postby hopeful_statguy » Tue Sep 22, 2009 11:51 pm

What edition do you have? In the 3rd edition, rule 3 is:
If a_1 \equiv b_1 \pmod{n} and a_2 \equiv b_2 \pmod{n} , then
a_1 \pm a_2 \equiv b_1 \pm b_2 \pmod{n}
a_1 a_2 \equiv b_1 b_2 \pmod{n}

kosuke
Posts: 5
Joined: Mon Aug 03, 2009 10:27 pm

Re: Princeton Review Error : Congruences Page 225

Postby kosuke » Thu Oct 29, 2009 4:52 pm

Sorry to bring this post back from the dead, but I'm having trouble figuring out what LeDuc meant to say here... (I think Legendre meant to say rule #4, not 3 on page 225).

Any idea on what LeDuc really means?

kosuke
Posts: 5
Joined: Mon Aug 03, 2009 10:27 pm

Re: Princeton Review Error : Congruences Page 225

Postby kosuke » Thu Oct 29, 2009 5:05 pm

Sorry, nevermind.

I figured out what I was doing wrong.

Legendre
Posts: 217
Joined: Wed Jun 03, 2009 1:05 am

Re: Princeton Review Error : Congruences Page 225

Postby Legendre » Fri Aug 24, 2012 6:31 am

Sorry I meant rule 4, not 3.

I think he meant that a = b (mod n) then, a = b or b + n or b + 2n or ... or b + (c-1)n (mod cn).

This is clear because for b + cn, b + (c+1)n,... we can mod out the cn and obtain same expression in the list.




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