Calendar: 1870-1871 Page 522

522 GENERAL LITERATURE AND SCIENCE 15 yz ג xy 59 ar 45 J4 3y xy3 19 2ע xy -f Eliminate ג ζ between tbe equations τ ί ד ζ χ ζ χ Define xm wben is an integer and prove that jr" "זג where and η are integers Define the arithmetical and geometrical means between two given numbers Prove that no two unequal numbers can have their arithmetical and geometrical means equal 10 In how many ways can £4 lis 6d be paid by means of half-guineas and half-crowns 11 Investigate rule for transforming mixed number from one scale of notation to another Transform 723 from the denary to the duodenary scale 12 If AaB when is constant and AaC when Β is constant prove that aBC when Β and vary together 13 Find the number of ways in which mn things can be divided among persons so that each shall have of thein 14 In converging fractions η qn pn Reduce -2 to continued fraction Prove that the difference between two numbers with the same digits is divisible by 15 Find the number of ways in which η different things can be given to ρ persons so that each person may have one at least Find also the number of ways in which η indifferent things can be given to ρ persons both with and without this restriction 16 Prove the binomial theorem for positive integral index Prove that 2" CT ו