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Prove the following statement for non-zero integers a, b, c, If a divides b and b divides c, then a

Prove the following statement for non-zero integers a, b, c, If a divides b and b divides c, then a divides c. If an integer a divides an...
Thread by: math_celebrity, Feb 14, 2024, 0 replies, in forum: Calculator Requests

Prove the sum of any two rational numbers is rational

Take two integers, r and s. We can write r as a/b for integers a and b since a rational number can be written as a quotient of integers We can...
Thread by: math_celebrity, Jan 31, 2024, 0 replies, in forum: Calculator Requests

If a is an even integer and b is an odd integer then prove a − b is an odd integer

If a is an even integer and b is an odd integer then prove a − b is an odd integer Let a be our even integer Let b be our odd integer We can...
Thread by: math_celebrity, Jan 28, 2024, 0 replies, in forum: Calculator Requests

Prove that the difference of two consecutive cubes is never divisible by 3

Take two consecutive integers: n, n + 1 The difference of their cubes is: (n + 1)^3 - n^3 n^3 + 3n^2 + 3n + 1 - n^3 Cancel the n^3 3n^2 + 3n + 1...
Thread by: math_celebrity, Jan 24, 2024, 0 replies, in forum: Calculator Requests

Prove that the difference between alternate consecutive squares as always even

Take an integer n. The next alternate consecutive integer is n + 2 Subtract the difference of the squares: (n + 2)^2 - n^2 n^2 + 4n + 4 - n^2...
Thread by: math_celebrity, Jan 21, 2024, 0 replies, in forum: Calculator Requests

Prove the difference between two consecutive square numbers is always odd

Take an integer n. The next consecutive integer is n + 1 Subtract the difference of the squares: (n + 1)^2 - n^2 n^2 + 2n + 1 - n^2 n^2 terms...
Thread by: math_celebrity, Jan 19, 2024, 0 replies, in forum: Calculator Requests