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kathrynag
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Show that if R is an integral domain with characteristic p>0, then for all a,b in R, we must have (a+b)^p=a^p+b^p. Show by induction that we must also have (a+b)^p^n=a^p^n+b^p^n for all positive integers n.
R is an integral domain, so ab=0 implies a=0 or b=0.
The smallest positive integer n such that n*1=0 is called the characteristic of R.
R is an integral domain, so ab=0 implies a=0 or b=0.
The smallest positive integer n such that n*1=0 is called the characteristic of R.