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 A^2 = B^3 + C^3
 Set {4,b,c,d,e} such that the product of any two of them increased by 1 is a square
 smallest integer whose first n multiples all contain a 3
 Set {3,b,c,d,e} such that the product of any two of them increased by 1 is a square
 Set {2,b,c,d,e} such that the product of any two of them increased by 1 is a square
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Monthly Archives: November 2015
Divisibility puzzle : a*b*c  (a + b + c)^n, n = 7,13,21,31
Definition : If a and b are integers (with a not zero), we say a divides b if there is an integer c such that . we … Continue reading
Game theory  The Hunter’s Share
This game is a little more lifelike than the Prisoner’s Dilemma, as it involves more than two protagonists. The aim is to gain the most points, or ‘food’, after ten rounds or so. Imagine you are one of … Continue reading
Num3er 11296321
is a perfect square containing precisely one 3, two 2’s and three 1’s. Any of the other seven digits (0, 4, 5, 6, 7, 8, 9) occur only once. Find other examples. … Continue reading
Oblong numbers as a sum of two squares
A pronic number is a number which is the product of two consecutive integers, that is, a number of the form . They are also called oblong numbers. Prove that there are infinitely many positive integers … Continue reading
y = C(n, 7) – floor(n/7)
Show that… if then, is divisible by 7 is the largest integer not greater than x and is the smallest integer not less than x is the … Continue reading
a + b + c + a*b + b*c + c*a = a*b*c + 1
Find all triples of positive integers such that , and Solution: (a, b, c) = (2, 4, 13), (2, 5, 8), (3, 3, 7) … Continue reading
Four consecutive terms of an AP
We know that if you multiply any four consecutive positive integers and add 1 to the product, you’ll get a square number. The product of four consecutive terms of an arithmetic progression added to the fourth power of … Continue reading
y = (x!)^1/x
seems to be approaching a linear asymptote. Find an approximation for the equation of this line.
Grid 3×3 – Num3ers & Letters
5 22 18 28 15 2 12 8 25 rows: 5+22+18 = 45 28+15+2 = 45 12+8+25 = 45 columns: 5+28+12 = 45 … Continue reading