Wednesday, December 23, 2015

number theory - Prime factor of A=147+142+1




Find a prime factor of A=147+142+1. Obviously without just computing it.


Answer




Hint: I've seen the 3rd cyclotomic polynomial too many times.



x7+x2+1=(x7x4)+(x4+x2+1)=x4(x31)+x61x21=x4(x+1)(x2+x+1)+(x31)(x3+1)(x1)(x+1)=x4(x+1)(x2+x+1)+(x2+x+1)(x2x+1)



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