Question

if p=(102 power x) - (98 power x) and x is a natural number greater than zero. how many values exist at units place of p?

Answer 1

This is quite an interesting question

So,

Let us first analyse the units digits of 2 when the number is multiplied

(Why 2 , we are only dealing with the units digits of 102)

Now,

When 2 is multiplied consistently, the number at the units place will be

2

4

8

6

2

After this the values will repeat itself

Now,

For 98, we analyze 8

So,

8

4

2

6

8

After this the vales will repeat

Now,

We analyze the difference between the digits,

So, the following digits can be only obtained in the units place

4

6

8

0

2

So, these are five different values

Hence, five values will exist at the units place of p