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Let us divide the odd positive integers into two arithmetic progressions; the red numbers are 1,...

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Advance Math

Let us divide the odd positive integers into two arithmeticprogressions; the red numbers are 1, 5, 9, 13, 17, 21, ... The bluenumbers are 3, 7, 11, 15, 19, 23,....

(a) Prove that the product of two red numbers is red, and thatthe product of two blue numbers is red.

(b) Prove that every blue number has a blue prime factor.

(c) Prove that there are infinitely many blue prime numbers.Hint: Follow Euclid’s proof, but multiply a list together, multiplythe result by four, then subtract one.

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