b. Prove that the integer 359,240,758 cannot be a perfect quartic. (i.e. fourth power) that 250 758 Ppose

Q: Prove that a number in the form 6k+5,” what I mean is a number in the form of 6 times some integer…

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Q: Prove the square of any odd integer is expressible in the form 8n+1 with n ∈Z.

A:

Q: Prove that 5n-1 is divisible by 4 to any positive integer n

A:

Q: Show that every positive integer can be written as the product of a square (possibly 1) and a…

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Q: at any positive odd integer is of the

A: Here we have to show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5,…

Q: Prove that 3 divides 17k+1-2*5k+3+11k+3 whenever k is a nonnegative integer

A: The objective is to prove that 3 divides 17k+1-2*5k+3+11k+3 whenever k is a nonnegative integer

Q: 7) Use a direct proof to show that: a) The sum of an even integer and an odd integer is odd. b) If n…

A: Use the following concepts, to obtain the required result. An even integer m can be written as a…

Q: 5) Let n be a positive integer such that 7 | (8-1). Prove that 7 | (8=*1 - 1). (Hint: Rewrite 8*1…

A: Given: Let n be a positive integer such that 78n-1. To prove: 78n+1-1

Q: (3) Prove that if a cube of a number is divisible by 17, then the number is divisible by 17.

A: We have to prove that if cube of a any number is divisible by 17 then the number itself is divisible…

Q: 2. Prove that the difference of an odd integer and an even integer is odd.

A: Prove that the difference of an odd integer and an even integer is odd

Q: Justify that every prime number except 2 and 3 has the form 6q + 1 or 6q + 5 for some integer q.

A: Let ‘P ‘be any prime number Divide ‘p’ by 6, we get P=6q+r       - (1);     r=1,2,3,4,5 And q be any…

Q: Prove that the cube of any integer in the form 9k or 9k + 1 or 9k + 8 .

A: Let n be some integer then by the Division Algorithm, n = 3p , 3p+1 or 3p+2 for some integer p

Q: Show that if k is a positive integer, then (15k+4)/(10k+3) is in lowest terms.

A: We use the concept of Ring theory that a fraction is in lowest form if the gcd of numerator and…

Q: Prove that the fourth power of any integer has one of the forms 5k or5k + 1, where k is an integer.

A: We need to prove that any integer has one of the forms 5k or 5k + 1, where k is an integer.Let p be…

Q: . Show that if r is a nonzero real number, k and m are distinct integers, and ax and am are any real…

A: Given system is Crk+kDrk=akCrm+mDrm=am also given that r is non-zero real number and k and m are…

Q: Prove that no number of form 4k+3 (where K is a positive integer) can ever be the sum of two perfect…

A:

Q: Prove {12a + 4b : a and b are integers} = {4c : c is an integer}

A:

Q: Prove 8 divides 34h+1+52h+1 whenever h is a positive integer

A: We need to prove that 8 divides 34h+1+52h+1 whenever h is a positive integer by Mathematical…

Q: n2 - 2 is

A:

Q: Prove that no integer congruent to 3 modulo 4 can be written as the sum of two squares.

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Q: 3.) Which positive integers have an odd number of positive divisors?

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Q: Prove that 8" – 14n + 27 is divisible by 7, for all positive integers n.

A: The objective is to prove 8^n-14n+27 is divisible by 7.

Q: Prove that the number V7 lies between 1 and 2.

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.