[其他] 一題證明題請教～
Suppose p is an integer with p >= 2 and the following property:
for any two integers m,n if p|(mn) then either p|m or p|n (or both).
Show that p must be prime.
目前的想法是利用反證法：
Assume p is not a prime
We can write p = ab, where a, b are integers and not equal to 1
So gcd(p,n)=a and gcd(p,m)=b
Then a= px + ny and b = pq + mr
ab = (xb)a + (yb)n = (qa)p + (ra)m
再來就卡住了
跪求大家幫忙
謝謝
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