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 A^2 = B^3 + C^3
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 smallest integer whose first n multiples all contain a 3
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Monthly Archives: August 2014
Puzzle: Triangular numbers, n+p and T(n)+T(p)
Gary (republicofmath) found : (2) solve analytically
Patterns  (x + y + z)^n – (x^n + y^n + z^n); n = 2,3,5,7
in exponents being the prime numbers 2, 3, 5, 7 : Find out whether the pattern continues with n = 11, 13 … Continue reading
N = a^2 + b^2 + (a b) = c^2 + d^2 + (c d)
Find all integers below 10000 which are expressible in two ways: and For example, Let’s take the first few terms of the sequence 91, 133, 273, 343, 553, 651, 703, 871, 931, 1057, 1261, … Continue reading
x^n + y^n + z^n = u^n + v^n + w^n; n = 1,3
If and Is the statement true ? then then But if that is , , , , Since then when … Continue reading
x^4 – y^4 = z^3
—————————————— Contributor: David Radcliffe ——————————————
N = x^3 + y^2 = (a^3 + b^2)(c^2 + d^2)
To find such that where are nonzero integers for example, (1) Find more solutions Challenging question: (2) Generalize this
Patterns  (x + y)^p – x^p – y^p where p is a prime number
Let , , p is a prime number but so so So but so, Note the pattern: Determine —————————————— … Continue reading
(n, n+1) Higher Sum and Product
Among the distinct pairs of numbers whose sum is , the greatest possible product is Consider , find the distinct ways of achieving a higher product with two positive integers Here are the … Continue reading