Genady Posted November 5 Posted November 5 (edited) That is, 48 + 68 + 98. Edited November 5 by Genady 1
sethoflagos Posted November 5 Posted November 5 Spoiler Terms are first three terms of a geometric series a = 48, r = (3/2)8, n = 2 Sum = a (rn+1) -1) / (r -1) = 48 ((3/2)24 -1) / ((3/2)8 -1)) = 48 ((324 - 224) / (38 - 28) * (28 / 224)) = (324 - 224) / (38 - 28) = (316 + 38 28 + 216) (38 - 28) / (38 - 28) = 316 + 38 28 + 216 ...... which puts me back where I started!!!!! = (38 + 28)2 - 38 28 ....... aha! = ((38 + 28) + 34 24) ((38 + 28) - 34 24) = 8,133 x 5,521 Power is failing, so no time to check 1
Genady Posted November 5 Author Posted November 5 23 minutes ago, sethoflagos said: Hide contents Terms are first three terms of a geometric series a = 48, r = (3/2)8, n = 2 Sum = a (rn+1) -1) / (r -1) = 48 ((3/2)24 -1) / ((3/2)8 -1)) = 48 ((324 - 224) / (38 - 28) * (28 / 224)) = (324 - 224) / (38 - 28) = (316 + 38 28 + 216) (38 - 28) / (38 - 28) = 316 + 38 28 + 216 ...... which puts me back where I started!!!!! Of course. = (38 + 28)2 - 38 28 ....... aha! Yep, complete the square. = ((38 + 28) + 34 24) ((38 + 28) - 34 24) = 8,133 x 5,521 rather 8,113... Typo perhaps. +1
sethoflagos Posted November 6 Posted November 6 6 hours ago, Genady said: Typo perhaps Indeed. Neither factor can be divisible by 3.
TheVat Posted November 6 Posted November 6 Spoiler Looks like break everything down to powers of 2 and 3, then proceed algebraically. Would take some time but looks like subtract (24 x 34) from 38+28 and shouid give one factor. 6817 - 1296 = 5521. Rest is easy. 1
Genady Posted November 6 Author Posted November 6 +1. However, the "take some time" part can be accomplished in three steps, like this: Spoiler 216+28*38+316 = 216+2*28*38+316 - 28*38 = (28+38)2 - (24*34)2 = (28+38 + 24*34)*(28+38 - 24*34) which gives both factors at once. Is this what you've meant?
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