I have the following two congruence relations:
(1) $x^3\equiv 156417\pmod {262063}$
(2) $(7x+19)^3\equiv 6125\pmod {262063}$
And I need to solve this for x. I changed equation (2) into the following:
$343x^3 + 2793x^2 + 7581x\equiv 261329\pmod {262063}$
Then I tried filling in (1) into (2), so:
$343(k*262063 + 156417) + 2793x^2 + 7581x\equiv 261329\pmod {262063}$
And then I get:
$2793x^2 + 7581x\equiv 71150\pmod {262063}$
But I don't know if this is the way to go and I also don't know what to do with the other terms. Could someone please help me?