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A Pythagorean triplet (Posted on 2012-08-28) Difficulty: 3 of 5
Given that a2+b2 = c2
find the value of a*b*c if a+b+c=1000.

See The Solution Submitted by Ady TZIDON    
Rating: 5.0000 (2 votes)

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Some Thoughts Once in a lifetime opportunity | Comment 3 of 4 |

As this is likely the only chance I'll ever get to out-Charlie Charlie, I just can't resist posting all 84 solutions:-}

{{a == -499000, b == 999, c == 499001, x == -248752497501000}, {a == -249000, b == 998, c == 249002, x == -61877495004000}, {a == -124000, b == 996, c == 124004, x == -15314990016000}, {a == -99000, b == 995, c == 99005, x == -9752487525000}, {a == -61500, b == 992, c == 61508, x == -3752480064000}, {a == -49000, b == 990, c == 49010, x == -2377475100000}, {a == -30250, b == 984, c == 30266, x == -900897756000}, {a == -24000, b == 980, c == 24020, x == -564950400000}, {a == -19000, b == 975, c == 19025, x == -352438125000}, {a == -14625, b == 968, c == 14657, x == -207499149000}, {a == -11500, b == 960, c == 11540, x == -127401600000}, {a == -9000, b == 950, c == 9050, x == -77377500000}, {a == -5250, b == 920, c == 5330, x == -25743900000}, {a == -4000, b == 900, c == 4100, x == -14760000000}, {a == -3000, b == 875, c == 3125, x == -8203125000}, {a == -2125, b == 840, c == 2285, x == -4078725000}, {a == -1500, b == 800, c == 1700, x == -2040000000}, {a == -1000, b == 750, c == 1250, x == -937500000}, {a == -250, b == 600, c == 650, x == -97500000}, {a == 0, b == 500, c == 500, x == 0}, {a == 200, b == 375, c == 425, x == 31875000}, {a == 375, b == 200, c == 425, x == 31875000}, {a == 500, b == 0, c == 500, x == 0}, {a == 600, b == -250, c == 650, x == -97500000}, {a == 750, b == -1000, c == 1250, x == -937500000}, {a == 800, b == -1500, c == 1700, x == -2040000000}, {a == 840, b == -2125, c == 2285, x == -4078725000}, {a == 875, b == -3000, c == 3125, x == -8203125000}, {a == 900, b == -4000, c == 4100, x == -14760000000}, {a == 920, b == -5250, c == 5330, x == -25743900000}, {a == 950, b == -9000, c == 9050, x == -77377500000}, {a == 960, b == -11500, c == 11540, x == -127401600000}, {a == 968, b == -14625, c == 14657, x == -207499149000}, {a == 975, b == -19000, c == 19025, x == -352438125000}, {a == 980, b == -24000, c == 24020, x == -564950400000}, {a == 984, b == -30250, c == 30266, x == -900897756000}, {a == 990, b == -49000, c == 49010, x == -2377475100000}, {a == 992, b == -61500, c == 61508, x == -3752480064000}, {a == 995, b == -99000, c == 99005, x == -9752487525000}, {a == 996, b == -124000, c == 124004, x == -15314990016000}, {a == 998, b == -249000, c == 249002, x == -61877495004000}, {a == 999, b == -499000, c == 499001, x == -248752497501000}, {a == 1001, b == 501000, c == -501001, x == -251252502501000}, {a == 1002, b == 251000, c == -251002, x == -63127505004000}, {a == 1004, b == 126000, c == -126004, x == -15940010016000}, {a == 1005, b == 101000, c == -101005, x == -10252512525000}, {a == 1008, b == 63500, c == -63508, x == -4065020064000}, {a == 1010, b == 51000, c == -51010, x == -2627525100000}, {a == 1016, b == 32250, c == -32266, x == -1057227756000}, {a == 1020, b == 26000, c == -26020, x == -690050400000}, {a == 1025, b == 21000, c == -21025, x == -452563125000}, {a == 1032, b == 16625, c == -16657, x == -285784149000}, {a == 1040, b == 13500, c == -13540, x == -190101600000}, {a == 1050, b == 11000, c == -11050, x == -127627500000}, {a == 1080, b == 7250, c == -7330, x == -57393900000}, {a == 1100, b == 6000, c == -6100, x == -40260000000}, {a == 1125, b == 5000, c == -5125, x == -28828125000}, {a == 1160, b == 4125, c == -4285, x == -20503725000}, {a == 1200, b == 3500, c == -3700, x == -15540000000}, {a == 1250, b == 3000, c == -3250, x == -12187500000}, {a == 1400, b == 2250, c == -2650, x == -8347500000}, {a == 1500, b == 2000, c == -2500, x == -7500000000}, {a == 1625, b == 1800, c == -2425, x == -7093125000}, {a == 1800, b == 1625, c == -2425, x == -7093125000}, {a == 2000, b == 1500, c == -2500, x == -7500000000}, {a == 2250, b == 1400, c == -2650, x == -8347500000}, {a == 3000, b == 1250, c == -3250, x == -12187500000}, {a == 3500, b == 1200, c == -3700, x == -15540000000}, {a == 4125, b == 1160, c == -4285, x == -20503725000}, {a == 5000, b == 1125, c == -5125, x == -28828125000}, {a == 6000, b == 1100, c == -6100, x == -40260000000}, {a == 7250, b == 1080, c == -7330, x == -57393900000}, {a == 11000, b == 1050, c == -11050, x == -127627500000}, {a == 13500, b == 1040, c == -13540, x == -190101600000}, {a == 16625, b == 1032, c == -16657, x == -285784149000}, {a == 21000, b == 1025, c == -21025, x == -452563125000}, {a == 26000, b == 1020, c == -26020, x == -690050400000}, {a == 32250, b == 1016, c == -32266, x == -1057227756000}, {a == 51000, b == 1010, c == -51010, x == -2627525100000}, {a == 63500, b == 1008, c == -63508, x == -4065020064000}, {a == 101000, b == 1005, c == -101005, x == -10252512525000}, {a == 126000, b == 1004, c == -126004, x == -15940010016000}, {a == 251000, b == 1002, c == -251002, x == -63127505004000}, {a == 501000, b == 1001, c == -501001, x == -251252502501000}}

Edited on August 28, 2012, 12:51 pm
  Posted by broll on 2012-08-28 12:50:23

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