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4 Answers

 n = number
 
   n < 3000
 
   n = 32( p) + 30
 
   n = 58( q) + 44
 
    32( p ) + 30 = 58 ( q) + 44
 
   3000 - 30 = 32p
 
      P = 92     n = 2944
 
   2944 - 44 = 58 q     q = 50
 
     n = 2944
 
   

Comments

2944 does not work!
And I don't follow your steps ... ???
Let x be the number, all the other letters positive integers
x=32n+30
x=58m+44
32n+30=58m+44 and so
16n+15=29m+22
16n=29m+7
16n=16m+13m+7, so we need to find am m for which 13m+7 is divisible by 16.
Trial and error, I confess.  m=13 gives 169+7=176=16×11
x=58×13+44=798=32*24+30
There are other answers.
 
n/32 = Q + 30/32 => n = 32Q + 30
n/58 = P + 44/58 => n = 58P + 44 => n mod 58 = 44

Using an Excel SS (below) I found three numbers:

798, 1726, and 2654

But I don’t know how to do it otherwise; someone help!

Q n=32*Q+30 n mod 58 = 44?
1 62
2 94
3 126
4 158
5 190
6 222
7 254
8 286
9 318
10 350
11 382
12 414
13 446
14 478
15 510
16 542
17 574
18 606
19 638
20 670
21 702
22 734
23 766
24 798 YES
25 830
26 862
27 894
28 926
29 958
30 990
31 1022
32 1054
33 1086
34 1118
35 1150
36 1182
37 1214
38 1246
39 1278
40 1310
41 1342
42 1374
43 1406
44 1438
45 1470
46 1502
47 1534
48 1566
49 1598
50 1630
51 1662
52 1694
53 1726 YES
54 1758
55 1790
56 1822
57 1854
58 1886
59 1918
60 1950
61 1982
62 2014
63 2046
64 2078
65 2110
66 2142
67 2174
68 2206
69 2238
70 2270
71 2302
72 2334
73 2366
74 2398
75 2430
76 2462
77 2494
78 2526
79 2558
80 2590
81 2622
82 2654 YES
83 2686
84 2718
85 2750
86 2782
87 2814
88 2846
89 2878
90 2910
91 2942
92 2974
93 3006

Comments

Just trial and error that I did .

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