Jadhav Theorem/Examples

Examples of Use of Jadhav Theorem

Square of $102$

Consider the square of $102$.

Consider $102$ as a term in an arithmetic sequence:

$100$, $102$, $104$

whose common difference is $2$.

Then from the Jadhav Theorem:

$102^2 - 100 \times 104 = 2^2$

from which we have:

$102^2 = 100 \times 104 + 4 = 10404$

Square of $406$

Consider the square of $406$.

Consider $406$ as a term in an arithmetic sequence:

$400$, $406$, $412$

whose common difference is $6$.

Then from the Jadhav Theorem:

$406^2 - 400 \times 412 = 36^2$

from which we have:

$406^2 = 400 \times 412 + 36 = 164 \, 800 + 36 = 164 \, 836$