Fibonacci Numbers

Table[(((((1+(Sqrt[5])))^n)-(((1-(Sqrt[5])))^n))/((2^n) (Sqrt[5]))),{n,1,10}]

Simplify[%]

Linear Combination and Greatest Common Divisor

S=Table[2x-4y,{x,-3,3},{y,-2,2}]

T=Flatten[S]

U=DeleteDuplicates[T]

Sort[U]

Modulo Arithmetic

Mod[12,3]

Mod[-123,5]

Table[Mod[(2^n),7],{n,1,6}]

Table[Mod[(3^n),7],{n,1,6}]

Table[Mod[(4^n),7],{n,1,6}]

Table[Mod[(5^n),7],{n,1,6}]

Table[Mod[(6^n),7],{n,1,6}]

Periods of Fibonacci Numbers

Table[Fibonacci[n],{n,1,20}]

Table[Mod[Fibonacci[ n],2],{n,1,20}]

Table[Mod[Fibonacci[ n],3],{n,1,20}]

Table[Mod[Fibonacci[ n],4],{n,1,20}]

Table[Mod[Fibonacci[ n],5],{n,1,50}]

Table[Mod[Fibonacci[ n],6],{n,1,50}]

Table[Mod[Fibonacci[ n],8],{n,1,50}]

Table[Mod[Fibonacci[ n],10],{n,1,30}]

Fermat Little Theorem

Table[Mod[(n^2),3],{n,1,10}]

Table[Mod[(n^3),4],{n,1,10}]

Table[Mod[(n^4),5],{n,1,10}]

Table[Mod[(n^5),6],{n,1,10}]

Table[Mod[(n^6),7],{n,1,10}]