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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: March 2012
3X3 Grid Digits 1 to 9
To arrange the digits 1 to 9 in the 3×3 square in such a way that the number in the second row is twice that in the first row, and the number in the bottom row is three times that … Continue reading
A Fun Little Puzzle: 3X4 Grid 1 to 12 numbers
1 2 3 4 5 6 7 8 9 10 11 12 Object: To divide this grid into two parts so that the total sum … Continue reading
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Arranging Digits from 1 through 9 in Two Groups
The digits 1 through 9, are arranged in two groups. Each group represents a multiplication and, more interestingly, results in the same product 532 76 … Continue reading
Interesting Trigonometry Identities
I’m going to list trig. identities that I find interesting. I leave the proofs for the readers. I start with these two: (1) If α, β and γ are the angles of a right triangle, then sinα … Continue reading
If x is a Triangular number, then so is ax+b
Triangular number: Definition 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666, … Continue reading
12 = 3*4 and 56 = 7*8. Other examples?
12 = 3*4 and 56 = 7*8 are of the form: 10*a + (a + 1) = (a + 2)*(a + 3) 11a + 1 = (a + 2)*(a + 3) 11a + 1 = a^2 + … Continue reading
Sum of Consecutive Prime Numbers Under 1000
List of all prime numbers under 1000: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, … Continue reading
2 puzzles: Squares, Cubes & Prime Numbers
(1) Sum of the squares of the digits of a prime is another prime number For example, 11, 1^2 + 1^2 = 2 is prime the prime number 23, 2^2 + 3^2 = 13 the … Continue reading
Expressing Prime Num3ers by Using All Digits 1,2,3,4,5,6,7,8,9
Expressing Prime Num3ers using all digits from 1 to 9 only once From 1 to 9: (1) + 2 – 3 – (4 * 5) + (6 * 7) + 8 + 9 = 37 is a prime number … Continue reading
When Sums of Products of Prime Num3ers is a Power
A primorial, denoted n#, is the product of the first n prime numbers. The first 15 prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 1# = 2 2# = 2*3 = … Continue reading