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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!

#Mathematics #Class VII-X Mathematics

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Devil ·2009-08-05 10:22:14

I'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)

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