Soham has his $$23^{\text{rd}}$$ birthday on $$1^{\text{st}}$$ January $$2024$$ and he noticed that $$2024$$ is divisible by $$23$$. If he lives till $$100$$ years of age, how many times other than the above, his age would be a divisor of the then year?
Solution
Soham was born in $$2001$$, so at age $$n$$ the year is $$2001+n$$. The condition requires $$n$$ to divide $$2001+n$$, which is equivalent to $$n$$ dividing $$2001$$. Since $$2001=3\times 23\times 29$$, the future ages after $$23$$ and up to $$100$$ that work are $$29,69,87$$, giving $$3$$ more occasions.
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