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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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 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: August 2015
Find (x,y) so that (x+1)/y + (y+1)/x is a positive integer
You may want to prove the last statement. Advertisements
Solutions to x^2 ± x*y + y^2 = z^2
Solutions to when is an odd integer Generalize this.
Open question: Positive integers as a sum of squares and cubes?
Every positive integer is a sum of four squares (Lagrange’s Theorem) It is known that every positive integer is a sum of no more than 9 positive cubes, and that every “sufficiently large” integer is a sum of … Continue reading
Puzzle  ArithmeticMean() and HarmonicMean()
Let’s take the number 10 10 has 4 divisors: 1 2 5 10 Let’s compute the Arithmetic Mean and Harmonic Mean of (1, 2, 5, 10) Multiplying the two means: … Continue reading
floor(√x – √y) = floor(√17) where (x,y) are prime numbers
Here are solutions for y = 2, 3, 5, 7
Can you find a triangular number with exactly 500 divisors?
is the smallest triangular number which has 576 divisors Can you find a triangular number with exactly 500 divisors?
Diophantine Equation x^3 + y^3 + z^3 – 3 xyz = A^3
Case #1 : , , , and , Here are the first few examples: Case #2 : , , , and , Here are the first … Continue reading
Number of divisors: d(a)=8, d(b)=18 and ba=28 (sequence:8,18,28)
Let be the number of divisors of Find positive integers such that and and the smallest pair that satisfies the two conditions are (152, 180) : 152 … Continue reading
Puzzle Digit Permutations of 123,1234,12345,123456,…
By permuting the digits of the number 123, we obtain 6 different numbers: 123, 132, 213, 231, 312, 321 The sum of these numbers is : 123 + 132 … Continue reading