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In base 10 representation,every integer n is the sum of some multiples of the powers of 10.

By December 6, 2021No Comments

In 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 aak-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]2.An integer n is divisible by 3 if and only if the sum of its digits is divisible by 3.(Hint:Use modular arithmetic.What is 10 congruent to modulo 3?)[15 pts]

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