Prove that 4 does not divide a^2+2 for any integer a. b) Prove that there are no integers satisfying (x,y )=3 and x+y=100 . c) Find all primes that divide 50! . d) Prove the following (i) 10!=1 (mod11) (ii) 7|(2222^5555+5555^2222) iv)89|(2^44-1)
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