1 Number TheoryIn base 10 representation,every integer n is the sum of some multiples of the powers of 10.For example,ifn=12345,then n=1·104+2·103+3·102+4·101+5·10°.In general,if the digits of the base-10 representation of n form the string akak-1…ao,thenn=∑a·10.(1)i=01.Show that an integer n is divisible by 2 if and only if its last digit is even.(Hint:For each i≥1inEq.(1),102≡0(mod2).When ao is even,what is it congruent tomodulo 2?)[15 pts]
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