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. Br. xviii, 7; V. 160.

73. What square multiplied by eight and having one added to the product will be a square? V. 82.

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. Br. xviii, 67.

$\scriptstyle {(1)\ 92u^{2}+1=t^{2}\quad (2)\ 83u^{2}+1=t^{2}}$.

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? V. 87.

$\scriptstyle {(1)\ 67u^{2}+1=t^{2}.\quad (2)\ 61u+1=t^{2}.}$

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

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L=the Līlāvatī, V=Vīja Gaņita, both by Bhāskara, M=Mahāvīra, S=Srīdhara, C=Chaturveda.