World!OfNumbers |
WON plate 193 | |
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[ Some have double, triple, quadruple, quintuple and even a sevenfold set of constituents. He used clever Excel table programming to get some selected (restricted) results where one of the two powers is an eight-digit number in the case of ninedigitals and a nine-digit number in the case of pandigitals (the 2nd powers are only resultants). The filtering and sorting was speeded up with the help of his grandson Puneeth and daughter in law Indira Ramesh. Alas, I cannot reproduce the programs in HTML, so I will stick to displaying partly results and some magical curios for some chosen categories but without the restrictions imposed by B.S. Rangaswamy. Interested and involving readers may try to discover existence of other strange constituents for any of the remaining vast number of nine- and/or pandigitals.
Statistical information and more curios are to be found in one of my dedicated ninedigits pages. Please visit also Statistics and curios
Case N.1 ninedigital = strictly single solutions for A^{2} + B^{2}
Case N.2 ninedigital = strictly double solutions for A^{2} + B^{2}
Solutions must be < 200000000.
Case N.3 ninedigital = strictly triple solutions for A^{2} + B^{2}Note that these triples are sparingly scattered.
More solutions exist. Case N.4 ninedigital = quadruple solutions for A ^{2} + B^{2}
strictly quadruple solutions for A^{2} + B^{2}
The next best thing is to search for them as
More solutions exist. Case N.5 ninedigital = quintuple solutions for A ^{2} + B^{2}
strictly quintuple solutions for A^{2} + B^{2}
The next best thing is to search for them as
strictly quintuple solution of this kind. It doesn't exist.
The next best thing is to search for them as
Case N.6 ninedigital = sextuple solutions for A ^{2} + B^{2}
strictly sextuple solutions for A^{2} + B^{2}
The next best thing is to search for them as
strictly sextuple solutions for A^{2} + B^{2}
The next best thing is to search for them as
Case N.7 ninedigital = sevenfold solutions for A ^{2} + B^{2}
strictly 7-fold solutions for A^{2} + B^{2}
The next best thing is to search for them as
But the first occurence happens within the following 16-fold ninedigital
strictly 7-fold solutions for A^{2} + B^{2}
The next best thing is to search for them as
Case N.8 ninedigital = eightfold solutions for A ^{2} + B^{2}
Case N.9 ninedigital = higher-fold solutions for A^{2} + B^{2}
Case N.N.1 Lowest and highest ninedigitals for A ^{2} + B^{2}
Case N.N.2 Apart from squares there are cubes & other powers as 2_tier constituents of ninedigitals but that will be a topic for a separate investigation in the future.
Case N.N.3 ninedigital = single solutions for A ^{3} + B^{2}
125734689 = 450 Case N.11 ninedigital = single solutions for A ^{4} + B^{2}
123497685 = 93
B.S. Rangaswamy wishes all of us a happy new year 2015 ( = 11
Case P.1 pandigital = single solutions for A Lots of solutions are known...
Case P.2 pandigital = double solutions for A ^{2} + B^{2}( A and B not restricted ). Many more solutions exist...
Case P.3 pandigital = triple solutions for A ^{2} + B^{2}.
Case P.4 pandigital = quadruple solutions for A ^{2} + B^{2}( A and B not restricted ).
Case P.5 pandigital = quintuple solutions for A ^{2} + B^{2}
Who can provide me with the first example ? Case P.6 pandigital = sextuple solutions for A ^{2} + B^{2}
Who can provide me with the first example ? Case P.7 pandigital = sevenfold solutions for A ^{2} + B^{2}
Who can provide me with the first example ? Case P.P.1 Lowest and highest pandigital for A ^{2} + B^{2}( A and B not restricted ).
Case P.P.2 Already one nice curio combining two numbertypes (pandigital) 1024397685 = 31482 ^{2} + 5769^{2} (ninedigital)Case P.P.3 More nice curios in case of higher exponents
Case P.P.4 ninedigital = double solutions for A ^{3} + B^{2}
Note: this list is very lengthy ! | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

A000193 Prime Curios! Prime Puzzle Wikipedia 193 Le nombre 193 |

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