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# How to factorize RSA modulus while given two Public Exponents and the difference between two Private Exponents?

The RSA modulus is the product of two $$2048$$-bit primes.

And the two Public Exponents are both $$16$$-bit.

I also got the difference between two Private Exponents $$\left | d_1-d_2 \right |.$$

Is there any way to factorize the Modulus $$N$$?

What is the origion of this Q? How much this difference?
diff/n is about 3n/5,I thought it looks like some special trick in Cryptanalysis of RSA with two decryption exponents
you mean absolute difference not difference divided by n clearly
So you know $N,e_1,e_2, |d_1-d_2|$ with small $e_1$ and $e_2$, and want to factor $N$. Hint: write a relation that must exist between $e_1$ and $d_1$, same between $e_2$ and $d_2$. If these contain$\bmod$, apply the definition of that to remove it. And proceed to adapt the [usual method to factor $N$ given $e$ and $d$](https://crypto.stackexchange.com/q/62482/555).
I sit in a Tesla and translated this thread with Ai: