Taking into consideration the title, a pythagorean triple should consist solely of positive integers and the answer is a=200, b=375, c=425; a*b*c=31,875,000.
However, based on the puzzle text, the following program also allows for negative integers:
DEFDBL A-Z
CLS
FOR tot = 2 TO 99999
FOR a = 1 TO tot / 2
b = tot - a
csq = a * a + b * b
c = INT(SQR(csq) + .5)
IF c * c = csq THEN
t = a + b + c
IF t >= 1000 THEN
IF t = 1000 THEN PRINT a; b; c, a * b * c
IF -a + b + c = 1000 THEN PRINT -a; b; c, -a * b * c
IF a - b + c = 1000 THEN PRINT a; -b; c, -a * b * c
IF a + b - c = 1000 THEN PRINT a; b; -c, -a * b * c
IF a - b - c = 1000 THEN PRINT a; -b; -c, a * b * c
IF -a + b - c = 1000 THEN PRINT -a; b; -c, a * b * c
IF -a - b + c = 1000 THEN PRINT -a; -b; c, a * b * c
END IF
END IF
NEXT
NEXT
and finds, up to the point where manually stopped:
a b c a*b*c
200 375 425 31875000
-250 600 650 -97500000
750 -1000 1250 -937500000
800 -1500 1700 -2040000000
840 -2125 2285 -4078725000
1625 1800 -2425 -7093125000
1500 2000 -2500 -7500000000
1400 2250 -2650 -8347500000
875 -3000 3125 -8203125000
1250 3000 -3250 -12187500000
1200 3500 -3700 -15540000000
900 -4000 4100 -14760000000
1160 4125 -4285 -20503725000
1125 5000 -5125 -28828125000
920 -5250 5330 -25743900000
1100 6000 -6100 -40260000000
1080 7250 -7330 -57393900000
950 -9000 9050 -77377500000
1050 11000 -11050 -127627500000
960 -11500 11540 -127401600000
1040 13500 -13540 -190101600000
968 -14625 14657 -207499149000
1032 16625 -16657 -285784149000
975 -19000 19025 -352438125000
1025 21000 -21025 -452563125000
980 -24000 24020 -564950400000
1020 26000 -26020 -690050400000
984 -30250 30266 -900897756000
1016 32250 -32266 -1057227756000
But clearly there are no further all-positive solutions, as we've reached the point where a+b alone equals 33266, much more than 1000.
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Posted by Charlie
on 2012-08-28 11:14:42 |
computer solution
