Çözüldü Divisibility - Odd and Even Numbers

How many different values larger than 10 can the remainder hold after a three-digit number xy5 is divided by 26?
https://www.facebook.com/photo.php?fbid=10157522775514518&set=gm.1659892637481606&type=3&theater&ifg=1
[Another solution by a math teacher Mr. Erkan Akça: The number of the two-digit odd numbers less than 26, because dividend (xy5) is odd, quotient multiplied by divisor (26) is even, so remainder must be odd.]
(Because the Facebook group where the problem was posted was set to "Private" on September 25, 2022, only members can see the original post and any other solutions.)

Starting from the lowest xy5 number as 105 with the remainder 1 in increments of 10;
115----11
125----21
135-----5 ( = 31 - 26)
145----15
155----25
165-----9 ( = 35 - 26)
175----19
185-----3 ( = 29 - 26)
195----13
205----23
215-----7 ( = 33 - 26)
225----17
*****************
235-----1 ( = 27 - 26)
...cycles

So, only 8 numbers which are 11, 13, 15, 17, 19, 21, 23, 25.