Euler Algebra and Prime numbers

Hi

I got two tasks which I have some trouble with.

1)

A guy has 1770 dollars to shop food for. One bread costs 31 dollars and a jar of jam costs 21 dollars.

How many loafs of bread and jar's of jam can the guy buy?

I'm suppose to calculate it using Euler Algebra

31x + 21y = 1770

Do I solve this by guessing x,y ?

2)

a) Show that an integer, is congruent 3 mod 4, and which has a prime factor which is congruent modulo with 4.

How do I do that?

b) show that infinit many prime numbers are congruent 3 mod 4.

Any idears?

Sincerely Yours MT

p.s. I'm going to hospital tomorrow for a operation with my heart, so therefore I hope that there is somebody out who could be so kind to help me answer these two questions.