if a and b are integers divisible by 4, the a^2+bc+a is a multiple of 4 for any integer c
a=4m where m is an integer
b= 4n where n is an integer
a(a+1)+bc= 4m(4m+1)+4nc= 4[m(m+1)+nc]
a2+bc+a is a multiple of 4 or divisible by 4
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