Polynomial Modulus Calculator

Question

I have the following polynomial equation. (3+65)x^4+(97)x^3+(8+97)x^2+(18+97)x+(24+97) mod 11971 = 11707, where x is a numeric base. I would like something to solve for x. The Wolfram languagewill do this. But, the required computation time for some of my desired values exceeds that allowed by the Wolfram language. Does someone know of a calculator that will perform this simplification task without having to pay for a subscription to Wolfram|Alpha Pro (or purchase a license for Mathematica, which I have used many times before, as the license costs over $300.00)?

Answer 1

You might be correct. Wolfram|Alpha returned 4 bases for 3,518. I will continue using Wolfram|Alpha for these, as 3,519 is only 1 of 9 values. Thank you, Dana.

Answer 2

>.." This would be true if I knew what the base was."

I'm afraid I don't understand.  Your question was " I would like something to solve for x"

 (3+65)x^4

I am also not sure why your equation looks so complicated.

=CODE("D")  ->   68

..etc

I also apologize.  For some reason, I thought Jo..2004 was asking the question.

= = = = = =

> ... replace 11,707 with 3,519. 

I may be wrong, but I don't think there is a solution for 3519.

I think the nearest number is 3518.

Using 3518 would have solutions of 3455, 8556, 10323, 11289

Answer 3

“Maybe an x value of 224 ?” This would be true if I knew what the base was. But, that is my objective exactly, to find the base. Specifically, I have a 5-character Unicode string that is represented by the following equation: (3+65)x^4+(97)x^3+(8+97)x^2+(18+97)x+(24+97) mod 11971 = 11707. What I want to know is this. When those characters are converted from a given base to decimal and that decimal result is divided by 11,971, I want the remainder to be a specific amount (that, by the way, is not 11,707). For one of my specific cases, use the same equation above, but replace 11,707 with 3,519. In what base does the decimal value yielded by the Unicode string Daisy (represented by the equation above), when divided by 11,971, yield a remainder of 3,519. According to Wolfram|Alpha, the decimal value for the Unicode string Daisy, when divided by 11,971, yields a remainder of 11,707 when converted from base-224. I hope this clarifies what I am trying to accomplish for you.

Answer 4

For the Integer solution, maybe an x value of 224

equ = (3 + 65) x^4 + (97) x^3 + (8 + 97) x^2 + (18 + 97) x + (24 + 97)

121 + 115 x + 105 x^2 + 97 x^3 + 68 x^4

' The equation with x at 224

172294424857

Mod(172294424857, 11971)

11707

Answer 5

Solver found a solution "instantly".

Enter the following formula in B1:

=MOD((3+65)*A1^4+(97)*A1^3+(8+97)*A1^2+(18+97)*A1+(24+97), 11971)

Of course, that can be simplified.  I just copy-and-pasted and replaced "x" with "*A1".

Then set up Solver as follows:

Objective: B1

To Value of: 11707

By Changing: A1

Solver derived the value 3.18683614882701, and the value in B1 is 11706.9999767619.

Good enough for me.  You can play with Solver options to improve the result in B1.  Sometimes, just running Solver again with its first value in A1 improves things.  (Not this time.)