Determine all possible triplets (p, q, r) of positive integers that satisfy this equation:
p
7 + q
3 = r
2, whenever
gcd (p, q, r) = 1
(In reply to
sub-spoiler by Ady TZIDON)
10 for R=1 to 1000000:T=R*R
20 for P=1 to int(T^(1/7))
30 for Q=1 to int((T-P^7)^(1/3)+0.5)
40 if P^7+Q^3=T then
50 :G=gcd(P,Q):G=gcd(G,R)
60 :print P,Q,R,G
70 next
80 next
90 next
finds
p q r gcd
1 2 3 1
3 9 54 3
2 17 71 1
8 64 1536 8
8 128 2048 8
9 243 4374 9
10 225 4625 5
9 486 10935 9
15 225 13500 15
...
so (2,17,71) also fits
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Posted by Charlie
on 2011-01-09 18:04:51 |
re: sub-spoiler--another, via computer
