Hey! I don’t get why 11y2 = 3 mod 17 turns into y2 = 8 mod 17. I don’t also get

Question

Hey!
I don’t get why 11y2 = 3 mod 17 turns into y2 = 8 mod 17.
I don’t also get why 808 mod 187 turns into 37 mod 187..
Can someone help?

Edit View History Bookmarks Window Help E Chegg Study TEXTBOOK SOLUTIONS EXPERT Q&A; E Chapter 4.3, Problem 4E 0 4Bookmark n. Through these system of congruences MM a mod m 17 24(mod 11) y 8(modIl) And I ly, 3(mod 17) y,=8(mod 17) Now, by Chinese Remainder theorem, required x is given as = 4.8. 1 7 + 3.8.1 I 808 x = 808 ( mod M ) 808 ( mod l 87 ) " 37(mod187) Therefore the solution of the given congruencies is # 37

Explanation / Answer

According to chinese reminder theorem we need to find an inverse for the value of 11 such that 11*inverse(11)/17 must give a reminder equal to 1.

Such an inverse is 14. i.e., 11*14 = 154 and the reminder we get after dividing this by 17 is 1.

now multiplying 11 y2=3 mod 17 on both sides by 14 we will get

y2 = 42 mod 17

and if we apply mod on 42 we will get 8....

i.e., 42 / 17 will give the reminder 8.

same procedure is applied for 808 mod 187.

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