3. Prove that least significant digit of the square of an even integer is either 0, 4, or 6.

Q: 32. Prove that 3 divides n³ +2n whenever n is a positive integer.

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Q: Find a positive integer n such that 2n is a square and 3n is a cube.

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Q: 10. Let x be a real number. Prove that at least one of the numbers /2 – x or /2 +x is irrational.

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Q: Prove that 6">5" + 9 for any integer n ≥ 2.

Q: s?

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Q: prove that the one's digit of any integer,n, is the remainder when one divides n by 10.

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Q: 2. Prove the statement: The sum of the squares of any two consecutive integers is odd.

Q: 3. Show that there exist 100 consecutive positive integers that are not perfect squares.

Q: 2. Use Fundamental Theorem of Arithmetic to prove that the product of any two odd integers is an odd…

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Q: show that no integer of the form n^3+1 is a prime other than 2