Good afternoon! If...

Questions
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1

Good afternoon! If in wolframalpha.com enter the query Solve [ (x^ 2) Mod 11= 0, x mod 61= 41, x] , then it correctly returns the answer x= 671 N+ 407 and n elements Z.
If you then click “Plain text” – “Wolfram language code”, will get the same query Solve[{ Mod[ x^2, 11] == 0, Mod[ x, 61] == 41} , x]. I click “COMPUTABLE NOTEBOOK” and try to run the query. I get the error {“Solve”, ""This system cannot be solved with the methods available to Solve.} What is the error and what am I doing wrong ? Thanks.

2

Try:

$Version
(*"12.1.0 for Microsoft Windows (64-bit) (March 14, 2020)"*)

Solve[{Mod[x^2, 11] == 0, Mod[x, 61] == 41}, x, Integers](*Or: Reals *)
(* {{x -> ConditionalExpression[407 + 671*C[1], Element[C[1], Integers]]}}*)

Regards M.I.

3

Thank a lot! It works!