Question 2.(2+6 points) Consider the equation 221x+ 377y=c. It is known that gcd(221,377) = 13 andthat 13 = (221)(12) + (377)(-7).(a) For which values ofcdoes the equation have an integer solution?

(b) Find all integer solutions for 221x+ 377y= 52.

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Question 3.(5+5 points)(a) It is known thata≡b(modm) iffa=b+mkfor somek∈Z. Use thisfact, or the definition of the congruence relation, to prove that ifa≡c(modm) andb≡d(modm), thenab≡cd(modm).