Using Euclid’s division algorithm, find the largest number that divides 1251, 9377 and 15628 leaving remainders 1, 2 and 3, respectively.
Prove that if x and y are both odd positive integers, then x2 + y2 is even but not divisible by 4.
Show that the square of any positive integer cannot be of the form 6m + 2 or 6m + 5 for any integer m.
Show that the square of any positive integer cannot be of the form 5q + 2 or 5q + 3 for any integer q.
Show that cube of any positive integer is of the form 4m, 4m + 1 or 4m + 3, for some integer m.
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