The following notation and terminology is useful. If a and b are integers, then
ID: 3109185 • Letter: T
Question
The following notation and terminology is useful. If a and b are integers, then a divides b, written a | b, if a notequalto 0 and there exists an integer k such that b = ak. Note that though one uses the term "divides" the definition refers only to the operation of multiplication of integers. It does not refer to any operation of "division." Thus, any proofs involving this notation should make use of the properties of multiplication of integers and not refer to "division." One also uses the terminology that b is a multiple of a if there exists an integer k such that b = ak. This latter terminology does not assume that a notequalto 0. However, if a notequalto 0, the statement "a divides b" is equivalent to the statement "b is a multiple of a." Prove that, if a, b and c are integers such that a^2 + b^2 = c^2, then at least one of a or b is a multiple of 3.Explanation / Answer
we have x2 = 0,1(mod3)
so a2+b2 = c2
the above box reveals that if the given condition satisfies then there is atleast one number among three squares which is congruent to 0 mod3. it implies it is divisble by 3.
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