Let a, b and c integers. Prove or disprove the next statements:

a.7|𝑎^7−𝑎
b.If 7|𝑎2+𝑏2 then 7|𝑎 and 7|𝑏
c.If 7|𝑎3+𝑏3+𝑐3 then 7|𝑎𝑏𝑐