n=661775625

FactorInteger[n]

3^2 5^4 7^6-n

GCD[2^15-1,2^20-1]

FactorInteger[2^15-1]

FactorInteger[2^20-1]

Expand[(a+b)^5]

Simplify[%]

Table[Binomial[5,r],{r,0,5}]

sol=Solve[x^2+a x+b==0,x]

x^2+a x+b/.sol

Simplify[%]

sol=Solve[x^3+p x+q==0,x]

sol/. -9q+Sqrt[3]Sqrt[4p^3+27q^2]-> A

%/.{1+I Sqrt[3]->-2om2,1- I Sqrt[3]->-2om}

% /. A->18u

{x1,x2,x3}=x/.sol;

x1

x2

x3

x^3+p x+q/.sol

Simplify[%]

f[x_]:=x^2 Sqrt[x]+(x^3-x)Sqrt[x^2+x+1]

D[f[x],x]

Simplify[%]

g1=Plot[%,{x,0,2}]

g2=Plot[(f[x+0.001]-f[x])/0.001,{x,0,2}]

Export["df.eps",g1]

Export["dfn.eps",g2]

Integrate[%,x]

%-f[x]

Simplify[%]

f[x_]:=Sqrt[(1+x^2)/(1-x^2)]

f'[x]

Simplify[%]

Integrate[%,x]

f[x_]:=1/(x-2)^5

Integrate[f[x],{x,0,1}]

-(15/64)l

y=Integrate[f[x],x]

(y/.x->1)-(y/.x->0)

D[y,x]

f[x_]:=1/(2+Cos[x])

Integrate[f[x],{x,0,Pi}]

y=Integrate[f[x],x]

Simplify[%]

(y/.x->Pi)-(y/.x->0)

Plot[y,{x,0,Pi}]

Simplify[%]

D[%,x]

%-f[x]

Simplify[%]