Genady Posted January 1, 2022 Share Posted January 1, 2022 The whole puzzle is in the title. It took a friend of mine, in his own words, "3 pages of factoring (correcting and replacing)". It took me 6 lines. Take a challenge? Link to comment Share on other sites More sharing options...
TheVat Posted January 2, 2022 Share Posted January 2, 2022 Would finding low prime factors be of any use? Maybe not. Link to comment Share on other sites More sharing options...
Genady Posted January 2, 2022 Author Share Posted January 2, 2022 9 minutes ago, TheVat said: Would finding low prime factors be of any use? Maybe not. I don't know how I would do this except by going backward, i.e. after finding the answer to the puzzle looking for its prime factors. Link to comment Share on other sites More sharing options...
Genady Posted January 2, 2022 Author Share Posted January 2, 2022 Step 1: 48 + 68 + 98 = 22*8 + 28*38 + 32*8 Link to comment Share on other sites More sharing options...
Genady Posted January 3, 2022 Author Share Posted January 3, 2022 Step 1: 48 + 68 + 98 = 22*8 + 28*38 + 32*8 Step 1.5: = (28)2 + 28*38 + (38)2 Link to comment Share on other sites More sharing options...
Genady Posted January 3, 2022 Author Share Posted January 3, 2022 On 1/1/2022 at 8:11 PM, TheVat said: Would finding low prime factors be of any use? Maybe not. Did you mean these "low prime factors" -- see the previous post? If so, I apologize. My mistake, I didn't understand you. You were right. From this point, you need only one "trick" more, and not a very uncommon one. Link to comment Share on other sites More sharing options...
Genady Posted January 3, 2022 Author Share Posted January 3, 2022 Step 1: 48 + 68 + 98 = 22*8 + 28*38 + 32*8 Step 1.5: = (28)2 + 28*38 + (38)2 Step 2: = (28)2 + 2*28*38 + (38)2 - 28*38 Link to comment Share on other sites More sharing options...
Genady Posted January 4, 2022 Author Share Posted January 4, 2022 Step 1: 48 + 68 + 98 = 22*8 + 28*38 + 32*8 Step 1.5: = (28)2 + 28*38 + (38)2 Step 2: = (28)2 + 2*28*38 + (38)2 - 28*38 Step 2.5: = (28 + 38)2 - (24*34)2 Link to comment Share on other sites More sharing options...
Genady Posted January 5, 2022 Author Share Posted January 5, 2022 Step 1: 48 + 68 + 98 = 22*8 + 28*38 + 32*8 Step 1.5: = (28)2 + 28*38 + (38)2 Step 2: = (28)2 + 2*28*38 + (38)2 - 28*38 Step 2.5: = (28 + 38)2 - (24*34)2 Step 3: = (28 + 38 + 24*34)(28 + 38 - 24*34) = 8113*5521 Link to comment Share on other sites More sharing options...
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