linear functions mod 25 that do something

//those 4 numbers come from https://pastebin.com/zxkAfrHd
//Edit: the 5th one also comes from there. I can count.

> ash boolean[int] mons; mons[453]=true; mons[465]=true; mons[1541]=true; mons[1576] = true; mons[1949]=true; boolean works; for i from 1 to 100{for j from 0 to 100{ works = true; foreach k in mons{ if((i*k+j)%25 != 3){works=false;break;}if(works){print(i+"x+"+j+" works");}}}}

1x+0 works
1x+25 works
1x+50 works
1x+75 works
1x+100 works
2x+22 works
2x+47 works
2x+72 works
2x+97 works
3x+19 works
3x+44 works
3x+69 works
3x+94 works
4x+16 works
4x+41 works
4x+66 works
4x+91 works
5x+13 works
5x+38 works
5x+63 works
5x+88 works
6x+10 works
6x+35 works
6x+60 works
6x+85 works
7x+7 works
7x+32 works
7x+57 works
7x+82 works
8x+4 works
8x+29 works
8x+54 works
8x+79 works
9x+1 works
9x+26 works
9x+51 works
9x+76 works
10x+23 works
10x+48 works
10x+73 works
10x+98 works
11x+20 works
11x+45 works
11x+70 works
11x+95 works
12x+17 works
12x+42 works
12x+67 works
12x+92 works
13x+14 works
13x+39 works
13x+64 works
13x+89 works
14x+11 works
14x+36 works
14x+61 works
14x+86 works
15x+8 works
15x+33 works
15x+58 works
15x+83 works
16x+5 works
16x+30 works
16x+55 works
16x+80 works
17x+2 works
17x+27 works
17x+52 works
17x+77 works
18x+24 works
18x+49 works
18x+74 works
18x+99 works
19x+21 works
19x+46 works
19x+71 works
19x+96 works
20x+18 works
20x+43 works
20x+68 works
20x+93 works
21x+15 works
21x+40 works
21x+65 works
21x+90 works
22x+12 works
22x+37 works
22x+62 works
22x+87 works
23x+9 works
23x+34 works
23x+59 works
23x+84 works
24x+6 works
24x+31 works
24x+56 works
24x+81 works
25x+3 works
25x+3 works
25x+3 works
25x+3 works
25x+3 works
25x+28 works
25x+28 works
25x+28 works
25x+28 works
25x+28 works
25x+53 works
25x+53 works
25x+53 works
25x+53 works
25x+53 works
25x+78 works
25x+78 works
25x+78 works
25x+78 works
25x+78 works
26x+0 works
26x+25 works
26x+50 works
26x+75 works
26x+100 works
27x+22 works
27x+47 works
27x+72 works
27x+97 works
28x+19 works
28x+44 works
28x+69 works
28x+94 works
29x+16 works
29x+41 works
29x+66 works
29x+91 works
30x+13 works
30x+38 works
30x+63 works
30x+88 works
31x+10 works
31x+35 works
31x+60 works
31x+85 works
32x+7 works
32x+32 works
32x+57 works
32x+82 works
33x+4 works
33x+29 works
33x+54 works
33x+79 works
34x+1 works
34x+26 works
34x+51 works
34x+76 works
35x+23 works
35x+48 works
35x+73 works
35x+98 works
36x+20 works
36x+45 works
36x+70 works
36x+95 works
37x+17 works
37x+42 works
37x+67 works
37x+92 works
38x+14 works
38x+39 works
38x+64 works
38x+89 works
39x+11 works
39x+36 works
39x+61 works
39x+86 works
40x+8 works
40x+33 works
40x+58 works
40x+83 works
41x+5 works
41x+30 works
41x+55 works
41x+80 works
42x+2 works
42x+27 works
42x+52 works
42x+77 works
43x+24 works
43x+49 works
43x+74 works
43x+99 works
44x+21 works
44x+46 works
44x+71 works
44x+96 works
45x+18 works
45x+43 works
45x+68 works
45x+93 works
46x+15 works
46x+40 works
46x+65 works
46x+90 works
47x+12 works
47x+37 works
47x+62 works
47x+87 works
48x+9 works
48x+34 works
48x+59 works
48x+84 works
49x+6 works
49x+31 works
49x+56 works
49x+81 works
50x+3 works
50x+3 works
50x+3 works
50x+3 works
50x+3 works
50x+28 works
50x+28 works
50x+28 works
50x+28 works
50x+28 works
50x+53 works
50x+53 works
50x+53 works
50x+53 works
50x+53 works
50x+78 works
50x+78 works
50x+78 works
50x+78 works
50x+78 works
51x+0 works
51x+25 works
51x+50 works
51x+75 works
51x+100 works
52x+22 works
52x+47 works
52x+72 works
52x+97 works
53x+19 works
53x+44 works
53x+69 works
53x+94 works
54x+16 works
54x+41 works
54x+66 works
54x+91 works
55x+13 works
55x+38 works
55x+63 works
55x+88 works
56x+10 works
56x+35 works
56x+60 works
56x+85 works
57x+7 works
57x+32 works
57x+57 works
57x+82 works
58x+4 works
58x+29 works
58x+54 works
58x+79 works
59x+1 works
59x+26 works
59x+51 works
59x+76 works
60x+23 works
60x+48 works
60x+73 works
60x+98 works
61x+20 works
61x+45 works
61x+70 works
61x+95 works
62x+17 works
62x+42 works
62x+67 works
62x+92 works
63x+14 works
63x+39 works
63x+64 works
63x+89 works
64x+11 works
64x+36 works
64x+61 works
64x+86 works
65x+8 works
65x+33 works
65x+58 works
65x+83 works
66x+5 works
66x+30 works
66x+55 works
66x+80 works
67x+2 works
67x+27 works
67x+52 works
67x+77 works
68x+24 works
68x+49 works
68x+74 works
68x+99 works
69x+21 works
69x+46 works
69x+71 works
69x+96 works
70x+18 works
70x+43 works
70x+68 works
70x+93 works
71x+15 works
71x+40 works
71x+65 works
71x+90 works
72x+12 works
72x+37 works
72x+62 works
72x+87 works
73x+9 works
73x+34 works
73x+59 works
73x+84 works
74x+6 works
74x+31 works
74x+56 works
74x+81 works
75x+3 works
75x+3 works
75x+3 works
75x+3 works
75x+3 works
75x+28 works
75x+28 works
75x+28 works
75x+28 works
75x+28 works
75x+53 works
75x+53 works
75x+53 works
75x+53 works
75x+53 works
75x+78 works
75x+78 works
75x+78 works
75x+78 works
75x+78 works
76x+0 works
76x+25 works
76x+50 works
76x+75 works
76x+100 works
77x+22 works
77x+47 works
77x+72 works
77x+97 works
78x+19 works
78x+44 works
78x+69 works
78x+94 works
79x+16 works
79x+41 works
79x+66 works
79x+91 works
80x+13 works
80x+38 works
80x+63 works
80x+88 works
81x+10 works
81x+35 works
81x+60 works
81x+85 works
82x+7 works
82x+32 works
82x+57 works
82x+82 works
83x+4 works
83x+29 works
83x+54 works
83x+79 works
84x+1 works
84x+26 works
84x+51 works
84x+76 works
85x+23 works
85x+48 works
85x+73 works
85x+98 works
86x+20 works
86x+45 works
86x+70 works
86x+95 works
87x+17 works
87x+42 works
87x+67 works
87x+92 works
88x+14 works
88x+39 works
88x+64 works
88x+89 works
89x+11 works
89x+36 works
89x+61 works
89x+86 works
90x+8 works
90x+33 works
90x+58 works
90x+83 works
91x+5 works
91x+30 works
91x+55 works
91x+80 works
92x+2 works
92x+27 works
92x+52 works
92x+77 works
93x+24 works
93x+49 works
93x+74 works
93x+99 works
94x+21 works
94x+46 works
94x+71 works
94x+96 works
95x+18 works
95x+43 works
95x+68 works
95x+93 works
96x+15 works
96x+40 works
96x+65 works
96x+90 works
97x+12 works
97x+37 works
97x+62 works
97x+87 works
98x+9 works
98x+34 works
98x+59 works
98x+84 works
99x+6 works
99x+31 works
99x+56 works
99x+81 works
100x+3 works
100x+3 works
100x+3 works
100x+3 works
100x+3 works
100x+28 works
100x+28 works
100x+28 works
100x+28 works
100x+28 works
100x+53 works
100x+53 works
100x+53 works
100x+53 works
100x+53 works
100x+78 works
100x+78 works
100x+78 works
100x+78 works
100x+78 works
Returned: void