What is this modular arithmetic question asking exactly?

**terrorsquid** · November 11th 2011, 08:50 PM

I just completed the first two parts of a question and am not sure how to use my answers in part c).

a) Write down an integer r which is divisible by 2611 and is congruent to 1 modulo 324

$r = 2611(-17) \equiv 1~mod~324$

b) Write down an insteger s which is divisble by 324 and is congruent to 1 modulo 2611

$s = 324(137) \equiv 1~mod~2611$

c) Consider the function $f : \mathbb{Z}_{845964}\rightarrow \mathbb{Z}_{2611}\times\mathbb{Z}_{324}$ given by:

$f(x~mod~845964)=(x~mod~2611,x~mod~324)$

Compute the value of $f(ar+bs)$

d)Deduce that $f$ is onto.

Is it perhaps notation that I don't understand that is asking me to find an integer x that satisfies both congruence equations?

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