(i) Solve the following simultaneous linear congruences: $$17x+23y ≡ 5\mod29$$$$ 10x+4y ≡ 11\mod29$$ (ii) If we were filling a 29 × 29 magic square using the uniform step method $$x_{j} ≡ 16+17j+23 \Bigl[\frac{j}{23}\Bigr]\mod29$$ $$y_{j} ≡ 9+10j+4\Bigl[\frac{j}{29}\Bigr]\mod29$$ Where [...] is the floor function.
What value of j would be placed in the cell with coordinates (21, 20)?
Hint What does (ii) have to do with (i)?
HINT
For (i), adding up the equations we obtain
$$27(x+y)\equiv 16 \mod {29}$$