Hint: Modulo 100I need help in working this out
View attachment 36674
No other hint is given. What I tried is looking for pattern by typing it to the power of 1 , 2 and 3 and so on, but it gets too large and incomputable. What other way can I use and how? Thank you
Hi BBBHint: Modulo 100
[math]17^{17} = 17^{16}\times 17[/math]Hi BBB
I tried this which gives 17, then I search for pattern
like 17^1 , 17^2 and so on, but the last two digits don't form any distinguishable pattern. Also I am not supposed to use calculator for this? can you give more hints/help?
What is [imath]17^2 \mod 100?[/imath]The only thing I understand is the indices property applied there, but I am lost can you help further?
89What is [imath]17^2 \mod 100?[/imath]
[imath]17^2 \equiv 89 \equiv -11 \mod 100[/imath]
Read post#8 again. You're not looking for a pattern, but leveraging prior modulo to find the subsequent ones. We don't need all of the even powers, only 2,4,8,16. You shouldn't need a calculator, only multiply 2 digits by 2 digits.View attachment 36679
I can't continue because the calculator won't display the last 2 digits anymore.
but I am not supposed to use calculator so this is probably not the right method also. But what am I seeing here? I don't see any pattern yet
The final answer is correct but your intermediate steps are not.I re-do the above working
View attachment 36680
please the me if this is correct, the last 2 digits are 77.
I use all the hints given above.
Maybe I missing something but I don't think your answer is correct as I don't see your answer.View attachment 36690
Thank you for correcting my steps, appreciate it as I am here not just for the answer, but for understanding how things work also mathematically
Thank you muchhhh Mr BBB.
Is the above correct ?
in post #11 I put 77, Mr Banana is correcting me on my steps.Maybe I missing something but I don't think your answer is correct as I don't see your answer.
An answer should look like the last two digits in 2017^2017 is _ _ !!!!!!
No, I won't accept your reply--sorryin post #11 I put 77, Mr Banana is correcting me on my steps.
noted, you have a point. Thank you so much for the adviseNo, I won't accept your reply--sorry
In post 13 you asked if the work in that post is correct.
If someone gives me some work to look at I would NEVER say that it is correct when it is incorrect just because the work they showed me before was correct.
D you read reply #2? SEE HEREI need help in working this out
View attachment 36674
No other hint is given. What I tried is looking for pattern by typing it to the power of 1 , 2 and 3 and so on, but it gets too large and incomputable. What other way can I use and how? Thank you