1. Exercise $1.5 #72. Definition: Let n and a be positive integers and let p be a prime number. Then p° is said to ezactly dieide n, denoted p | n, if p° |n and p+ { n. Assume that p° || m and p ||n. (a) What power of p exactly divides m+ n? Prove your assertion. (b) What power of p exactly divides mn? Prove your assertion. (c) What power of p exactly divides m"? Prove your assertion.

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1. Exercise $1.5 #72. Definition: Let n and a be positive integers and let p be a prime number.
Then p" is said to eractly divide n, denoted p" || n, if p" |n and ptl i n. Assume that p" || m and p' ||n.
(a) What power of p exactly divides m+ n? Prove your assertion.
(b) What power of p exactly divides mn? Prove your assertion.
(c) What power of p exactly divides m"? Prove your assertion.
Transcribed Image Text:1. Exercise $1.5 #72. Definition: Let n and a be positive integers and let p be a prime number. Then p" is said to eractly divide n, denoted p" || n, if p" |n and ptl i n. Assume that p" || m and p' ||n. (a) What power of p exactly divides m+ n? Prove your assertion. (b) What power of p exactly divides mn? Prove your assertion. (c) What power of p exactly divides m"? Prove your assertion.
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