MHB Divisors of $2^2.3^3.5^3.7^5$ & $7!$ in the Form of $4n+1$, $3t+1$

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The discussion focuses on finding the number of divisors of the expression $2^2 \cdot 3^3 \cdot 5^3 \cdot 7^5$ that fit the form $4n+1$, and also calculating the total number of positive divisors of $7!$ that fit the form $3t+1$. Participants are encouraged to share their approaches and any difficulties encountered in solving these problems. The conversation emphasizes the importance of understanding the properties of divisors in relation to specific modular forms. Engaging with these mathematical concepts can enhance problem-solving skills in number theory.
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(1) The number of divisers of the form $2^2.3^3.5^3.7^5$ which are is in the form of $4n+1$ where $n\in\mathbb{N}$

(2) Calculate Total no. of positive Divisers of $7!$ which are is in the form of $3t+1\;,$ where $t\in \mathbb{N}$
 
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jacks said:
(1) The number of divisers of the form $2^2.3^3.5^3.7^5$ which are is in the form of $4n+1$ where $n\in\mathbb{N}$

(2) Calculate Total no. of positive Divisers of $7!$ which are is in the form of $3t+1\;,$ where $t\in \mathbb{N}$

Hi jacks! :)

Where are you stuck?
Did you try anything?
 
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