Calendar: 1879-1880 Page 599

GENERAL LITERATURE AND SCIENCE 599 Show that the sum of the products of every pair of the first η natural numbers is 3w 24 Find the number of positive integral solutions of the equation ax -j- by where are integers Solve the equations χ χ yz z2 ax z2 ζ -j- by x2 -f xy -f- י ζ If κ be an integer so is 52 י-מ7 15 Sum the series to terms Every convergent to continued fraction is nearer to the value of the convergent than any preceding convergent Express 37 as continued fraction If the coefficient of xr in the expansion of נ where η is positive integer be denoted by φ prove that φ φ η φ φ η In an equation of the th degree in its simplest form if ρ be the greatest negative coefficient and η the highest power of which has negative coefficient as superior limit to the positive units 10 Iff be rational function of and prove tha tf is divisible by χ Thence prove that ζ ζ xy yf 2x'yV yf yz xz xyf