if a and b are two integers such that 7 divides a2+b2, prove that 49 divides a2+b2.
HINT:try using euclid's division algorithm
i must admit if presently i were in class ix-x, i would not even know how to approach it!
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1 Answers
11I'm hiding it....my soln should not be viewed for those trying it....
Point is from Fundamental theorem of arithmetic, min power of 7 in each a2 and b2 has to be 2.....The only case when 7| (a2+b2) is when 7 individually divides each....(Confirm by congruencies if necessary)....thus 49 | (a2+b2)