Prove: that if a is an odd integer, then 4 is a factor of a^2 -1

Q: Prove that the difference of squares of any two odd numbers is multiple of 8. (SOlve this task…

A: To proveDifference of squares of any two odd numbers is multiple of 8.

Q: Find all primes that are the difference of the fourth powers of two integers.

A: Let the two integers are x and y and n is prime so we have  n=(x4-y4)       (suppose x>y)…

Q: find a Positive integern for which the equality holds %3D

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Q: rove that the negative of any even integer is even

A: Assume 2n to be an even integer. 2n = even integer -2n = negative of even integer  Let a = -2n be an…

Q: Use a direct proof to show that the product of two odd integers is odd.

A: Introduction: A direct proof is a series of statements, the final of which is the conclusion to be…

Q: 6) find all the and non residues (mods) incongruent quadratic residues

A: It is given that Incongurant quadratic residues.

Q: Give a construction of a field with 16 elements.

A:

Q: Give a combinatorial interpretation of the coefficientof x6 in the expansion (1 + x + x2 + x3 +⋯)3.…

A: According to the given information, it is required to give a combinatorial interpretation of the…

Q: LI) Prove that (3

A:

Q: Prove that 279,930 is divisible by 7 using Fermat's Little Theorem.

A: We have to prove that 279930 is divisible by 7 using Fermat's Little theorem. The Fermat's little…

Q: Give a combinatorial interpretation of the coefficientof x4 in the expansion (1 + x + x2 + x3 +⋯)3.…

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: Expand in binomial theorem (2x-y)7

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Q: Find the remainder using Fermat’s Little theorem 452 mod 11.

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Q: Compute the last digit of 20072009 in two ways: (a) By combining Fermat's Little Theorem with the…

A: ANSWER:

Q: The sum of all positive integers less than 300 which are divisible by 3.

A:

Q: Prove that an odd number multiplied by an odd number is odd.

A: The objective is to prove that an odd number multiplied by an odd number is odd.

Q: Define an odd number and show that the product of odd even numbers is also even.

A: We need to first define an odd number. And layer prove product of an odd and an even number is…

Q: Suppose that Hilbert’s Grand Hotel is fully occupied on the day the hotel expands to a second…

A: We know, Hilbert's Grand Hotel is a thought experiment which gives counterintuitive property of…

Q: Prove that there are 1000 consecutive positive integers that are not perfect squares.

A: Here I give an example. That proves the hypothesis.

Q: Prove that the sum of the squares of two odd integers cannot be the square of an integer.

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Q: A positive integer n is called superperfect if ơ(ơ(n) = 2n Show that 16 is superperfect.

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Q: how to prove √6 is irrational

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Q: "Every positive integer can be written as the sum of the square of 3 positive integers." prove…

A: Given: "Every positive integer can be written as the sum of the square of 3 positive integers." To…

Q: The 4th term of an ap is zero. Prove that 25th term of the AP is three times its 11th term

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Q: (4) Prove that there is no smallest positive real number.

A: I have to prove that there is no smallest positive real number . Suppose that there is a smallest…

Q: The sum of all positive integers less than 300 which are not divisible by 3.

A: Sum of n positive integer is given by, Sn=nn+12

Q: 2. Prove that the Cartesian product N Nis countable

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Q: Describe a general method for finding all the divisors of a positive integer once you know the prime…

A: Given  A positive Integer whose prime factorization is given . To find all the divisors with general…

Q: Prove ZDBF LEBF

A: To prove: ∠DBF≅∠EBF

Q: the 20 1, 2, 3 Factor the number 211 – 1 by Fermat's factorization method. -

A: Fermat’s Factorization method is based on the representation of an odd integer as the difference of…

Q: Prove: The product of 2 numbers is equal to the product of their least common multiple and their…

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Q: if two even integers are multiflied, then the product is also even

A: Ans. True

Q: Show that the product of two numbers of the form 4n + 1 is still of that form. Hence show that there…

A:

Q: The sum of all positive integers less than 400 which are divisible by 5.

A: Positive integers less than 400 which are divisible by 5 are⇒n=79 5,10,15,20,...,395 The above…

Q: Which term of the expansion of (x + 7)° contains x° Term number contains x°.

A:

Q: Find odd and general

A: Given,       f(x)=x-π3;   0≤x≤π

Q: Prove this Adams-Bashforth method using polynomial interpolation and prove it's second order…

A: As per the question  we have to derive the two-step Adams-Bashforth method by using polynomial…

Q: Use syntheti division t deknnime k= -i in a zero of explaiin. fex)=x*+2x²+3X +2 the functui and

A:

Q: Find the ordinary generating function for the sequence 0,0,0,0,1,1,1...(Hint: it is not a…

A: We need to find an ordinary generating function. The sequence is 0,0,0,0,1,1,1,.... Consider:…

Q: Obtain the expansion of : 2 up to the term in x8 1-3x2

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Q: Find the product of - 10 - 6i and its conjugate. Question Help: DPost to forum

A: Given -10-6i

Q: Find two positive integers such that the four times loo0 and the product large as possible. the .…

A:

Q: "There is no largest integer."

A: Given: To explain the given statement as follows,

Q: Show that the set of all polynomials with integer coefficients is denumerable

A: Given : set of polynomial with integer coefficient  To Show : set of polynomial with integer…

Q: Use Fermat’s little theorem to find the least residue of 863 modulo 31.

A: Fermat's little theorem says: ap≡p(mod p)gcd(a,p)=1

Q: 9. Prove that the greatest common divisor of two positive integers divides their least common…

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Q: Prove that the difference of squares of any two odd numbers is múltiple of 8. (SOlve this task…

A: To prove- The difference of square of any two odd numbers is a multiple of 8.   Odd numbers are…