thepillow
New member
- Joined
- Sep 12, 2012
- Messages
- 34
I'm struggling with the following question:
Construct an element of order 103 in the multiplicative group of residues mod 1237.
If we let \(\displaystyle G \) denote the multiplicative group of residues mod 1237, then from what I understand the order of an element \(\displaystyle g \in G \) is the smallest \(\displaystyle n \) such that \(\displaystyle g^{n} \equiv 1 \mod{1237} \). If that's right then I need to find a \(\displaystyle g \in G \) such that \(\displaystyle g^{103} \equiv 1 \mod{1237} \).
But I'm not sure how to proceed from here, or if this is even a good way to approach the problem. I would be immensely grateful for any tips.
Thanks!
Construct an element of order 103 in the multiplicative group of residues mod 1237.
If we let \(\displaystyle G \) denote the multiplicative group of residues mod 1237, then from what I understand the order of an element \(\displaystyle g \in G \) is the smallest \(\displaystyle n \) such that \(\displaystyle g^{n} \equiv 1 \mod{1237} \). If that's right then I need to find a \(\displaystyle g \in G \) such that \(\displaystyle g^{103} \equiv 1 \mod{1237} \).
But I'm not sure how to proceed from here, or if this is even a good way to approach the problem. I would be immensely grateful for any tips.
Thanks!