lean_workbook_plus_17718

But $x^3 \equiv y^3 \pmod{10}$ implies $x^3 \equiv y^3 \pmod{2}$ , and so $x \equiv y \pmod{2}$ . Also $x^3 \equiv y^3 \pmod{10}$ implies $x^3 \equiv y^3 \pmod{5}$ , and so $x \equiv y \pmod{5}$ . Together, they yield $x \equiv y \pmod{10}$ , as claimed.