Question

write the sequence of natural numbers which leaves the remainder 3 on dividing by 5 and 10​

Answer 1

We have to find the sequence of natural numbers which leaves the remainder 3 when divided by 5 and 10.

Natural numbers are all counting number i.e., 0 to ∞

So, Let us find the first number after 0 that when divided by 5 and 10 leaves remainder 3.

The numbers should be divided by 10 and 5, then it is clear that the first number must be greater 10 and 5. Which is 13, obviously.

Any number which is divisible by 10 will also be divisible by 5. So we have to find the numbers which when divided by 10 leaves remainder 3.

First number is 13, so we should keep adding 10 to it to get the sequence of as many numbers as we want.

Which is,

⇒ 13, 23, 33, 43, 53, 63, 73, 83, ...

Which can also be expressed in a set builder form as:

⇒ { 10n + 3 ; n ∈ N}

Some Information :-

☞ Integers are collection of all positive and negative numbers including 0.

☞ Rational numbers are the numbers which can be expressed in the form of p/q where p & q are integers and q ≠ 0.

Answer 2

Question:-

write the sequence of natural numbers which leaves the remainder 3 on dividing by 5 and 10

Solution:-

• The descriptive solutions provided by others are very accurate, but to solve these type of questions without actually solving it, assume some values.
• Now a number when divided by 5 leaves a remainder 3. So easiest is assume the number to be 3.

then 3/5 => Remainder 3

now 3²/5 => Remainder 4

Next consider another number which leaves a remainder 3, when divided by 5, say 13.

then 13/5 => Remainder 3

now 13²/5 => Remainder 4

So we can safely generalize the answer to be 4.