Page:Indian mathematics, Kaye (1915).djvu/81

 72. What number divided by six has a remainder of five, divided by five has a remainder of four, by four a remainder of three and by three one of two? Answer—59. 73. What square multiplied by eight and having one added to the product will be a square? Here $$\scriptstyle{8u^2+1=t^2}$$ and u=6, 35, etc. t=17, 99, etc. 74. Making the square of the residue of signs and minutes on Wednesday multiplied by ninety-two and eighty-three respectively with one added to the product an exact square; who does this in a year is a mathematician. $$\scriptstyle{(1)\ 92u^2+1=t^2\quad (2)\ 83u^2+1=t^2}$$. Answer—$$\scriptstyle{(1)\ u=120,\ t=1151.\quad (2)\ u=9,\ t=82}$$. 75. What is the square which multiplied by sixty-seven and one being added to the product will yield a square-root; and what is that which multiplied by sixty-one with one added to the product will do so likewise? Declare it, friend, if the method of the 'rule of the square' be thoroughly spread, like a creeper, over thy mind? $$\scriptstyle{(1)\ 67u^2+1=t^2.\quad (2)\ 61u+1=t^2.}$$ Answers—(1) u=5967, t=48842. (2) u=226,153,980, t=1,766,319,049. 76. Tell me quickly, mathematician, two numbers such that the cube-root of half the sum of their product and the smaller number, and the square-root of the sum of their L=the Līlāvatī, V=Vīja Gaņita, both by Bhāskara, M=Mahāvīra, S=SrīdharaŚrīdhara [sic], C=Chaturveda.