Question 253639
Let htu be a three digit number. Since the numbers are consecutive, we have h_h-1_h-2 
in decreasing form or
h_h+1_h+2 in increasing form.
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decreasing order will not produce any answers.
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increasing :
This can be expressed as h(100) + (h+1)(10) + h+2. Now

(i) S^2 + 2 = h(100) + (h+1)(10) + h+2   
(ii) S^2 = 100h +11h + 10                
(iii) S^2 = 111h + 10                    
If h = 1, then 
S^2 = 111 + 10 = 121
S = 11.
The number is 123
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(v) h(100) + (h+1)(10) + h+2 = s^3 - 2 
(vi) 100h +11h + 14 = S^3
(vii) 111h + 14 = S^3
If h = 1, then
S^3 = 111 + 14 = 125
S = 15.
The number is 123.