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#### Resources tagged with Binomial Theorem similar to Powerful Factors:

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### Remainder Hunt

##### Stage: 5 Challenge Level:

What are the possible remainders when the 100-th power of an integer is divided by 125?

### Elevens

##### Stage: 5 Challenge Level:

Add powers of 3 and powers of 7 and get multiples of 11.

### Tens

##### Stage: 5 Challenge Level:

When is $7^n + 3^n$ a multiple of 10? Can you prove the result by two different methods?

### Summit

##### Stage: 5 Challenge Level:

Prove that the sum from t=0 to m of (-1)^t/t!(m-t)! is zero.

### Binomial

##### Stage: 5 Challenge Level:

By considering powers of (1+x), show that the sum of the squares of the binomial coefficients from 0 to n is 2nCn

### Growing

##### Stage: 5 Challenge Level:

Which is larger: (a) 1.000001^{1000000} or 2? (b) 100^{300} or 300! (i.e.factorial 300)

### Discrete Trends

##### Stage: 5 Challenge Level:

Find the maximum value of n to the power 1/n and prove that it is a maximum.

### Bina-ring

##### Stage: 5 Challenge Level:

Investigate powers of numbers of the form (1 + sqrt 2).