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I have encountered the same problem with my stainless steel pots and the cause is usually salt (added to boiling water for pasta, and other dishes), which can cause the white discoloration and sometimes 'pitting' of the stainless; unfortunately, it is permanent. This white discoloration may also be caused by hard water spots, when the pots dry, and if you have cleaned the pots in your dishwasher, this can also be caused by residue and/or tiny scratches caused by the abrasive action (if you use a tablet or powder) from the dishwasher detergent.
The discoloration you described, will not adversely affect the performance of the pots, or the foods cooked in them.
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