Monthly Archives: December 2014

Squared 10-tuples (a,b,c,d,e,f,g,h,i,j)

  Older post:   Squared 9-tuples (a,b,c,d,e,f,g,h,i)   To find 10-tuples     such that are square numbers.     9-tuples :   (3, 4, 12, 84, 204, 1428, 3468, 24276, 58956) gcd(3, 4, 12, 84, 204, 1428, 3468, 24276, … Continue reading

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Concatenation| Sum of consecutive integers: a+b+…+n = a||n

        Find other solutions   Manan Shah found:   David found: 203   +   202   +   …   +   28   =   20328   =   203 || 28 217   + … Continue reading

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Pythagorean triples with hypotenuse = 333,3333,…

  To find recurrence relations (whenever possible) with the following triples:     Here’s, for example, a recurrence relation for   (660,   3267,   3333)                      

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Pythagorean Triangle – lesser known formula

  (a, b, c)   is a Pythagorean triple shortest leg   =   a longest leg   =   b Let the perimeter be     and     the area.       since     and   Hence, … Continue reading

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N base-a = DigitReversal(N) base-b

    475   decimal   =   733   base-8   =   337   base-12 1337   decimal   =   935   base-12   =   539   base-16                                                                ——————————————   some examples where the … Continue reading

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Squared 9-tuples (a,b,c,d,e,f,g,h,i)

  To find 9-tuples     such that are square numbers.   Here are the first few examples:   (3, 4, 12, 84, 204, 1428, 3468, 24276, 58956) gcd(3, 4, 12, 84, 204, 1428, 3468, 24276, 58956) = 1 (3, … Continue reading

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Squared 8-tuples (a,b,c,d,e,f,g,h) and gcd(a,b,c,d,e,f,g,h) = 1

  To find 8-tuples     such that are square numbers.   Here are the first few examples:   (3, 4, 12, 84, 204, 1428, 3468, 24276)        gcd(3, 4, 12, 84, 204, 1428, 3468, 24276) = 1 (3, 4, … Continue reading

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Squared 7-tuples (a,b,c,d,e,f,g) and gcd(a,b,c,d,e,f,g) = 1

  To find 7-tuples     such that are square numbers.   Here are the first few examples:   (3, 4, 12, 84, 204, 1428, 3468)        gcd(3, 4, 12, 84, 204, 1428, 3468) = 1 (3, 4, 12, 84, … Continue reading

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Squared 6-tuples (a,b,c,d,e,f) and gcd(a,b,c,d,e,f) = 1

    To find 6-tuples     such that are square numbers.   Here are the first few examples:   (3, 4, 12, 84, 204, 1428)        gcd(3, 4, 12, 84, 204, 1428) = 1 (3, 4, 12, 84, 204, … Continue reading

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Squared 5-tuples (a,b,c,d,e), gcd(a,b,c,d,e) = 1

  To find 5-tuples   (a, b, c, d, e)   such that   a   <   b   <   c   <   d   <   e gcd (a, b, c, d, e)   =   … Continue reading

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