prove that the given statement is false . there exists an integer m>or=3 such that m^2 - 1 is prime

Q: let x  be a fixed but arbitrary integer. Do there exist infinity many integer y such that,…

A: Let x = x0 be fixed given integer. Then,

Q: Find the smallest positive integer n such that 5 (3² +2²) (3ª +2¹) (3³ +2³)... (3² +22") > 9256

A:

Q: Find the number of ways a 5-digit positive integer can be made such that in each of them every digit…

A:

Q: Suppose a is an integer. Prove that if a^3 is a multiple of 3, then a is a multiple of 3.

A: Let a3 is a multiple of 3 but a is not a multiple of 3.a3 is a multiple of 3Therfore, 3 divides…

Q: How many zeroes are at the end of 1000!/(500!500!)?

A: Calculate number of zeroes in 1000! and then subtract it from the number of zeroes in (500!500!).

Q: Prove that if x is an even integer, thenx^2−6x+ 3is odd

A: Any integer of the form 2m+1 is odd.

Q: Suppose that a particular real number has the property that (x + (1/x)) is an integer. Use (strong)…

A: Given that x+1x is an integer. We have to prove that xn+1xn is an integer for all natural number n…

Q: Prove that 18000 + 28000 38000 Theorem (and not a calculator). 18000 + 58000 + +4° 8000 is a…

A:

Q: prove if a and b are both odd integer, then 16/ (a^4) + (b^4) -2.

A:

Q: Prove that the messenger number M19 is a prime hence the integer n = 218 (219 -1) is perfect

A:

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.