Solving $t_1a_1^2+t_2a_2^2+...+t_na_n^2 = b.C^2$

Solving $t_1a_1^2+t_2a_2^2+...+t_na_n^2 = b.C^2$

Postby Guest » Sun Sep 23, 2018 6:39 pm

Given n,b,$t_i$

solve $t_1a_1^2+t_2a_2^2+...+t_na_n^2 = b.C^2$

Example for n=5, b=6 solve $1.a_1^2+2.a_2^2+3.a_3^2+4.a_4^2+5.a_5^2 = 6.C^2$

$1.77^2+2.61^2+3.67^2+4.2^2+5.4^2=6.67^2$

Example for n=4 , b=7, $t_i=1$ solve $a_1^2+a_2^2+a_3^2+a_4^2 = 7C^2$

$47^2+38^2+37^2+75^2=7.39^2$

I devised a parametric form to solve easily these forms but before post it, I would like to know if this method already exists, if possible author, book or else to read. I don´t remember this problem on Dickson and some other books I read.

Thanks

Miguel
Guest
 

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