Let-A-be-a-set-of-16-positive-integers-with-the-property-that-the-product-of-any-two-distinct-numbers-of-A-will-not-exceed-1994-Show-that-there-are-two-numbers-a-and-b-in-A-which-are-not-relatively-p

FacebookTweetPin

Question Number 21962 by Tinkutara last updated on 07/Oct/17

$$\mathrm{Let}A\mathrm{be}\mathrm{a}\mathrm{set}\mathrm{of}16\mathrm{positive}\mathrm{integers}$$$$\mathrm{with}\mathrm{the}\mathrm{property}\mathrm{that}\mathrm{the}\mathrm{product}\mathrm{of}$$$$\mathrm{any}\mathrm{two}\mathrm{distinct}\mathrm{numbers}\mathrm{of}A\mathrm{will}$$$$\mathrm{not}\mathrm{exceed}1994.\mathrm{Show}\mathrm{that}\mathrm{there}\mathrm{are}$$$$\mathrm{two}\mathrm{numbers}a\mathrm{and}b\mathrm{in}A\mathrm{which}\mathrm{are}$$$$\mathrm{not}\mathrm{relatively}\mathrm{prime}.$$

Commented by Rasheed.Sindhi last updated on 08/Oct/17

$$\mathrm{Possible}\mathrm{set}\mathrm{of}\mathrm{maximum}\mathrm{length}$$$$\left(\mathrm{i}\right)\mathrm{whose}\mathrm{elements}\mathrm{are}\mathrm{pairwise}$$$$\mathrm{coprime}\mathrm{and}$$$$\left(\mathrm{ii}\right)\mathrm{whose}\mathrm{product}\mathrm{of}\mathrm{any}\mathrm{two}$$$$\mathrm{elements}\mathrm{does}\mathrm{not}\mathrm{exceed}1994$$$$\mathrm{is}\mathrm{of}\mathrm{length}14\mathrm{and}\mathrm{is}\mathrm{as}\mathrm{follows}:$$$$\{2,3,5,7,11,13,17,19,23,29,31,37,41,43\}$$

Commented by Tinkutara last updated on 08/Oct/17

$$\mathrm{Thank}\mathrm{you}\mathrm{very}\mathrm{much}\mathrm{Sir}!\mathrm{Now}\mathrm{solved}.$$

Terms of Service
Privacy Policy
Contact: info@tinkutara.com

FacebookTweetPin