(b) Prove that 32n²+1, for n ≥ 1.

Q: Find the remainder when x51 is divided by x + 4 in Z7[x].

A: We have to find the remainder when x51 is divided by x+4 in Z7x. Let t be the remainder when x51 is…

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Q: Indicate the least integer n such that (3x5 + x²)4 = 0(x¹). E

A:

Q: n(n-1) 2 this statement to justify the following. (n+³) = - :)-( (equation 1). 2 (n + 3)(n + 2) 2…

A:

Q: (d) Show that 1 + √2 is a unit in R and use this to conclude that R has infinitely many units. (e)…

A: To show that 1+2 is a unit in R , we need to find its inverse in R. Let a+b2 be the inverse of 1+2…