## (a, b, c); a*b = 1 (mod c)

Consider   $(2, \; 3, \;5)$

$(2\times 3) \;\equiv \; 1 \; \pmod{5}$
$(3\times 5) \;\equiv \; 1 \; \pmod{2}$
$(5\times 2) \;\equiv \; 1 \; \pmod{3}$

Can you find another triplet with the same property?

that is,

$(a, \; b, \; c)$   such that

$(a\cdot b) \;\equiv \; 1 \; \pmod{c}$
$(b\cdot c) \;\equiv \; 1 \; \pmod{a}$
$(c\cdot a) \;\equiv \; 1 \; \pmod{b}$